From The Life of The Right Honourable Francis Bacon, Baron of Verulam, Viscount Saint Alban by William Rawley, D.D., His Lordship's First and Last Chaplain and of Late His Majesties Chaplain in Ordinary, 1657:
Towards his rising years, not before, [Francis Bacon] entered into a married estate, and took to wife Alice, one of the daughters and coheirs of Benedict Barnham, Esquire and Alderman of London; with whom he received a sufficiently ample and liberal portion in marriage. Children he had none; which, though they be the means to perpetuate our names after our deaths, yet he had other issues to perpetuate his name, the issues of his brain; in which he was ever happy and admired, as Jupiter was in the production of Pallas Athena.
Neither did the want of children detract from his good usage of his consort during the inter-marriage, whom he prosecuted with much conjugal love and respect, with many rich gifts and endowments, besides a robe of honour which he invested her withal; which she wore unto her dying day, being twenty years and more after his death.
From Personal History of Lord Bacon from Unpublished Papers by William Hepworth Dixon, 1861. pp. 158-161: ....So again with his marriage to Alice Barnham. Lord Campbell makes merry over his mercenary love and his match of convenience. Yet from his own text, and from the pages of Montagu, it is certain that he knows nothing of this love or of this match; neither who Alice Barnham was, not the circumstances of her parents; neither when she became Bacon's wife, nor the amount of jointure which she brought home to her lord. He imagines that Alice became Lady Bacon in 1603, shortly after July 3d. He says she was rich.
In all that relates to Alice Barnham the writers of Bacon's life have been as much at fault as though she had been first the love and then the wife of Ward the Rover or Steer the Leveller, in place of being, as she was, lady to a man who framed the New Philosophy and held the Great Seal. Yet some of the facts about her birth, the associations of her early years, the members of her family, the circumstances of her love, courtship, marriage, and wedded life, may still be recovered from the manuscript mounds of the Bodleian, the State Paper Office, and the library of Westwood park.
More than a year ago, in writing to his cousin Cecil, Bacon mentioned his having found a handsome maiden to his mind. She loved him and he loved her. But her mother, a widow and again a wife, having made two good matches for herself, has set her heart on making great alliances for her girls. In part to please her, still more to glorify his bride, Bacon waits and toils that he may lay at her feet a settled fortune and a more splendid name.
The family into which—when he can steal an hour from the courts of law and the pursuits of science—he goes a-courting, and in which he is now an accepted lover, consists of four girls, their pretty mother, and a bold, handsome, heady step-father of fifty-six,—a group of persons notable from their private stories, and of romantic interest from their loves and feuds with the philosopher, and from the part they must have had in shaping his views of the felicities and infelicities of domestic life.
The four young girls are the orphan daughters of Benedict Barnham, merchant of Cheapside and alderman of his ward; an honest fellow who gave his wife a good lift in the world, and left his children to take their chance of rising among men, who, with all their sins, are never blind to the merits of women blessed with youth, loveliness, and wealth. Alice is the first to fall in love; but the three hoydens who now romp around her, and perhaps get many a hug and kiss from her famous lover, will soon be in their turns followed for their bright eyes and brighter gold. Elizabeth will marry Mervin Touchet, Earl of Castlehaven, that miserable wretch who, when his first young wife, the hoyden of to-day, is in her grave, will expiate on the block the foulest crime ever charged against an English peer. The two little things now playing at Alice's knee will become, in due time, Lady Constable and lady Soames.
From Wikipedia, the free encyclopedia: Alice Barnham was born 14 May 1592, to Benedict Barnham and his wife Dorothea, née Smith. Benedict Barnham (1559-1598) was a London merchant, who held the positions of Alderman, Sheriff of London (1591-1592), and Member of the English Parliament for Yarmouth. His father had been Sheriff before him. Her mother, Dorothea, or Dorothy (d. 1639), was the daughter of Humphrey Ambrose Smith, an important Cheapside mercer and the official purveyor of silks and velvets to Queen Elizabeth. Alice was the second of a family of daughters, her sisters being Elizabeth, Dorothy, and Bridget; a fifth, Benedicta, died at the age of 16 days. Her father died 4 April 1598, when Alice was not even six, but Alice was apparently a favourite, as his will said:
I give to my daughter, Alice Barneham, my lease of certain lands at Moulsham and Chelmsford in the County of Essex. And if it happen that the same Alice doe die and unmarried then I give the same lease to Elizabeth my eldest daughter, etc.
Her mother was also left well off, with legacies of land and plate, and quickly remarried, to Sir John Pakington of Worcestershire, 22 November 1598. After John died in 1625, she would remarry again, two more times, to Robert Needham, earlier that year made 1st Viscount Kilmorey, and when he died in 1631, Thomas Erskine, Earl of Kellie.
Her older sister Elizabeth Barnham (1591-1623) married Mervyn Tuchet, 2nd Earl of Castlehaven, who would become infamous for his depravity. The third sister married Sir John Constable, a friend of Bacon's, and the fourth married Sir William Soames.
After her father's death, Alice was brought up in the family of Sir John Pakington, who was a great favourite of Queen Elizabeth, known as "Lusty Pakington" for his magnificence of living. He owned several estates that hosted royalty, including King James I of England on his way from Scotland to take possession of the English throne in 1603. The family's favourite home was in the Strand, London.
Bacon's letters begin mention of Alice Barnham, 3 July 1603, an Alderman's daughter, an handsome maiden to my liking, when she was only eleven. They were engaged three years, and married 10 May 1606, before Alice turned fourteen, at St Marylebone's Chapel, a suburb to the North of London, with the reception at the Strand estate. She brought an income of £220 a year from her father's estate, and expected more after the death of her mother.
Alfred Dodd, in Francis Bacon's Personal Life-Story (Rider & Company: London, 1949) says their marriage was political:
Bacon had saved himself three years previously from being excommunicated altogether from the public service by his readiness for an engagement with a child of eleven years (Alice Barnham), a commoner. He was now going to open the door to State offices by his marriage to the "handsome wench" of thirteen, according to his bargain with the King and Cecil.
The Bacons' early married life was disturbed several times by quarrels between Sir John Pakington and Dorothy, when Dorothy would appeal to her powerful son-in-law, and Francis Bacon would try to stay out from between them. Once Bacon was even a judge on the High Commission and had to reject a lawsuit from Dorothy against John which had put John in prison.
Alice Bacon and her mother Dorothy were both reported by contemporaries as having extravagant tastes, and being interested in wealth and power. However, early in the marriage, Bacon had money to spare, "pouring jewels in her lap", and spending large sums on decorations. Power was also available, as in March 1617, along with Francis Bacon being made temporary Regent of England, a document was drawn up making Lady Bacon first lady in the land, taking precedence over all other Baronesses (it is not clear whether it was signed into law).
Their marriage led to no children. In 1620, she met Mr. John Underhill, and Mr. Nicholas Bacon, gentlemen-in-waiting at York House, Strand, Bacon's London property. She was rumoured to have had an ongoing affair with Underhill. Underhill was a cousin of the William Underhill who sold New Place to William Shakespeare in 1597.
In 1621, Bacon was accused of taking bribes, heavily fined, and removed from Parliament and all offices. Lady Bacon personally pleaded with the Marquis of Buckingham for the restoration of some of Bacon's salary and pensions, to no effect. They lost York House and left the city in 1622.
Reports of increasing friction in the marriage appeared, with speculation that some of this may have also been due to financial resources not being as abundantly available to Alice as she was accustomed to in the past. Alice was reportedly interested in fame and fortune, and when reserves of money were no longer available, there was constant complaining about where all the money was going. Various authors have written that there were indications that Francis was secretly funding the publishing of materials for the Freemasons, Rosicrucians, "Spear-Shakers", "Knights of the Helmet", as well as publishing (with the assistance of Ben Jonson) a selection of the plays he had written under the pen name of "Shake-Speare" in a "First Folio" in 1623.     
In 1625, Bacon became estranged from his wife, apparently believing her of adultery with Underhill. He rewrote his will, which had been quite generous to her, leaving her lands, goods, and income, to revoke it all:
"What so ever I have given, granted, conferred, or appointed to my wife in the former part of this my Will, I do now for just and great causes, utterly revoke, and make void, and leave her to her right only."
Less than two weeks after Bacon's death from pneumonia on 9 April 1626, Alice Barnham Bacon married Mr. John Underhill, at the Church of St Martin in the Fields, London, 20 April 1626. Soon after, 12 July 1626, Charles I of England knighted him at Oatlands.
They lived together at Old Gorhambury House, St Albans, Hertfordshire.
The Viscountess St Albans, as she still preferred to be called, spent much of her marriage in Chancery proceedings, lawsuits over property. The first year was over her former husband's estate, trying to get what was left of Bacon's property, without his much greater debts. She was opposed in this by Sir John Constable, her brother in law, who had held some of the estate in trust. In 1628 she filed suits for property owned by her late father. In 1631, she and her husband both filed suit against Nicholas Bacon, of Gray's Inn, their former friend, who had married Sir John Underhill's niece, and gotten Underhill to sign an agreement for a large dowry and extensive property, including some property of Alice that Sir John did not have rights to, and could only inherit after her death. Their petition to court stated that Bacon had tricked Underhill "who was an almost totally deaf man, and by reason of the weakness of his eyes and the infirmity in his head, could not read writings of that nature without much pain," to sign a paper not knowing what it contained.
In 1639, Viscountess St Albans and Sir John Underhill became estranged, and began to live separately. In a later lawsuit, after her death, Underhill blamed Robert Tyrrell, or Turrell, their manservant, for this alienation of affections. In her will of 1642, she left half her property to Turrell, and other property to her nephew, Stephen Soames. She was buried in the old Parish Church of Eyworth, Bedfordshire, 9 July 1650, near her mother, and her sister, Lady Dorothy Constable.
Much more information about Alice is available in The Life of Alice Barnham Wife of Sir Francis Bacon, by Alice Chambers Bunten. London: Oliphants, Ltd., 1919, 1928.
She died, childless, in 1650 and was buried on July 9 in the Parish Church of Eyworth, in Bedfordshire. The register reads: Alice, Viscountess Saint Alban, Widdowe Dowager to Francis Viscount Saint Alban, Lord Chancellor of England, was buried in Ye Church of Eyworth on the South Side therof the 9th July, 1650.