Sorry to have come late to this. Your Ashbys were one of the most famous Quaker families in the south of England, and the Quakers keep quite stupendous records of their members. Thus Edward Milligan who used to work in the Library at Friends House in London, has compiled a quite amazing book of reference called: Biographical dictionary of British Quakers in commerce and industry 1775-1920. I strongly recommend that anyone with Quaker ancestry should buy this book. It is available in paperback (although a weighty tome) for around £30 from the bookshop at Friends House, and it is worth every penny of that. It lists in alphabetical order all known UK Quakers working in commerce and industry, and usually gives dates for them, their parents, the names of their wives and their parents and dates, and information about their careers and children too. I can't praise it highly enough. I am not typing out the entry, but extracting the genealogical data:
I can tell you from the book that your ancestor was Thomas Ashby born 1733 died 1813, and that he had a number of careers including mealman, brewer and banker. He was born at Warborough, north of Benson 7 June 1733, and he was the son of Robert Ashby (1699/1700-1781) of Shillingford and Mary Ashby (whose maiden name was Lamb, born 1707/8-1794).
His wife was Hannah Wickens (1734-1818).There were four sons and five daughters of the marriage. One assumes that her parents weren't Quakers, as her father was a physician, and at this time Quakers were still not allowed to go to University or into the professions.
Among the children of Thomas Ashby b 1733, Mr Milligan mentions Mary (born 1758) who married Simeon Warner Hagen (1751-1812). There was also a Thomas Ashby born 1762 son of Thomas Ashby b 1733, and a Thomas Ashby born 1786, son of Thomas Ashby born 1762. Finally another Thomas Ashby born 1825 was the son of Thomas Ashby born 1786. Ancestors can have had no idea what pain and confusion they engender by passing the same name on for generation after generation!
Edward Milligan quotes another publication, The History of Barclays Bank, printed 1926, which appears to be a source of information about your family.
It would be very much worth your while to obtain a copy of the Milligan book, as I think you could certainly compile a family history of Thomas Ashby's generation and the succeeding one, just from the information in the book, all of which should be verifiable from the Quaker records. The fact that Quakers were not supposed to "marry out" at this time, means that there are likely to be connections with other Quaker families for all of hose who stayed within the Society of Friends. For example, Simeon Warner Hagen has his own entry in the book. He is shown as a skinner and miller, born at Tooley Street in Southwark, London, only son of Simeon Hagen b 1722.
I know there are connections between the Ashbys of Staines and Quaker families in my home town of Uxbridge, Middlesex. At least one of the Hull family of Uxbridge married into the Ashbys of Staines. At one point the meetings were circulating from Uxbridge to Staines, and so there are a lot of connections.
I will gladly copy out the relevant information for you but can't until after Thursday as I have a talk about the Quakers of Uxbridge to write and deliver. After that, if you need me to, I would be happy to do that for you.
best wishes
Fee