Hi Marton,
I've done a bit more research - and found a couple of things on my tree.
I found the following records which may - or may not - be relative to your Fosters:
Sarah Eversley married Cutler Beckett on 21/9/1822
Mary Priest married Cutler Beckett on 11/9/1866
I shouldn't think there were 2 Cutler Becketts - but there might have been! Both were marriages in Tring. It could be that he married twice - as Mary Priest did.
On my tree I have a John Becket who married Sarah Cutler on 27/1/1795. They had possibly Elizabeth Beckett b.8/1/1801 (c. 25/12/1849), and possibly Thomas Beckett c. 7/8/1796 and possibly George Becket c. 4/11/1798 (d. 11/10/1801)
All in Tring. I say possibly as the Family Search records say the parents were John Becket and Sarah who were the parents of these children - so I presume they were John Beckett and Sarah Cutler. I am wondering if Cutler Beckett was their son too (connecting their surnames) as I can't find any record of Cutler Beckett's birth. A lot of the records at this time went missing.
Sarah Cutler was daughter of John Cutler (B.1748) and Ann Bull (b.1752) who were married on 11/10/1773. She had brothers and sisters, the majority of whom went into the canvas weaving business and owned properties etc in Akeman Street, and Frogmore End. So I think the connection is via Cutler Beckett. The family at this point gets very interesting, all about the canvas weaving etc and the various connections between the big families in Tring at that time.
Have you any more names/information that you could tell me as there might be more connections? Who came from Ivinghoe and Bucks for instance?
Anyway, I'm tired now after all that searching

I will be in touch again
Diana