Elizabeth - I have no connection as far as I am aware with the Westleys of West Ham, although of course there maybe! I am researching the Westleys of Islington and particularly the family of George and Sarah Westley. George and Sarah moved to Islington from Piddington in Northamptonshire. You will see a descendants tree on my website which is located on Genealogy.com. I hope that it is of interest to you even if we are unable to make a connection.
I have numerous research results on the Westleys and on occassions I have noted those in the West Ham area, just in case. If there is anything in the information that I have that you would like to know then please let me know.