I have some info. on a Welch family from the Sevenoaks area which includes a William. Details are:
William Welch born abt 1776 at Sundridge - ag lab
Married Lucy Whitehead - no marriage record yet found
Daughter Sophia (Sofey/Sophie) Welch born 1808 Sundridge - this is my line
Other children George (who is listed as blind in 1851), Silas, Stephen, William, Mary, ? Elvy (note that the last two children may actually be Sophia's but were illegitimate and lived with William and Lucy)
I have some more info. on Sophia and her children plus details of who William worked for if you think there's any connection. We haven't been able to go further back so far.
Best wishes
Karin