(ex CB) m. (1) Elizabeth Barkham, (2) Jane Lowe.

Sir John Ramskill Twisden notes in his book, p. 181:
"William [Twysden] married on the 13th June 1665 Frances, only daughter and heir of Josias Crosse [1].  Josias Crosse died before his daughter's marriage; nothing is known of him but that he left behind him considerable house property in London, Southwark and Surrey, bought presumably with the profits of business in London.  His wife, Frances Garrard, was the daughter of Sir John Garrard, Baronet [2], whose family combined commercial pursuits in London with the ownership of an estate in the country, at Lamer [nr Wheathampstead] in Hertfordshire."
There are two footnotes to this:
[1] "At St Swithin's Church, Cannon Street.  See Addit MS. 34163, fo. III V."
[2]"Some particulars of the Garrard family will be found in Sir William Twysden's note-book (Addit MS 34168, fo. 64)."

From the above date and from Burke's extinct baronetcies, 2nd edition, pub 1841, p. 214, it looks likely that the John Garrard, Baronet was the first baronet.  Burke gives this John a total of 6 sons and 8 daughters but only names 2 of these.  To his son, another John Garrard, 2nd bart, Burke lists 8 children, none of whom is a Frances, indicating she was unlikely to be his daughter.
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TFPL, Oct 2003: In Boyd's Inhabitants of London, he lists, possibly from a parish of Clutterford (or Clutterbush?), Herts, the following 12 children:
1 Sir John m. 1636 Jane Lambard
2 Netherwill
3 Edward
4 William
5 Charles
1 Jane      m. 1634 Sir Justinian Soham
2 Elizabeth   m. 1646 Tottenham
3 Isabel
4 Margaret
5 Frances
6 Anne
7 Mary

Boyd also says there was a funeral certificate for Sir Edward Barkham in Herts Gen 2 / 336.

I wonder if this John Garrard remarried after the death of his first wife; his youngest child could have been little more than a year old when Eliz Barkham died.
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TFPL, Nov 2003: On IGI there is a record of a Jane Lowe who m. this John Garrard on 3 Jun 1638 at Westcombe, Kent.  Jane is reported to be the daughter of Thomas Lowe and Anne Coulston, and she is said to have been born in 1592, Christened on 16 Mar 1592/3 at St Peter's, London and buried on 22 Feb1692/3 also at St Peter's London.  Definitiely worthy of follow-up as she would explian who the mystery Dame ____ Garrard was on Frances' Marriage Allegation.

However... further digging on IGI shows that Jane Lowe also m. Moulton Lambard and their daughter Jane Lambard m. John Garrard, the son of the John G. that Jane Lowe is supposed to have married.  While this sort of thing was not uncommon, I wonder what really happened?

Burke's Commoners corroborates that John G. m. 2ndly the relict of Moulton Lambard but says that her name was Elizabeth.  So I am now reasonably assured that this second wife was the "mother" of Frances who consented to her marrying Josiah / John Cross.  Obviously it would be nice also to find some record of John G.’s marriage with her and thereby find her name.
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Complete Baronetage says the marriage was on 6 May 1611.

Complete Baronetage says the marriage was on 3 Jun 1636.