Hi Sally,
Some very interesting information there, I never knew that there was a Buer Road in London (perhaps I should look at the A-Z). I have sent you an invite to my family tree, from there you should be able to access the notes on individual Buers (in the case of William Buer b. 1749 the notes are quite large including a transcript of his Will which leaves things to most of his living relatives - so very useful).
I have not yet updated my tree with your branch of the family, but if you go from William Buer b. 1749, via his son William b. 1783, then you get to William b. 1813 who was Willaim Beaumont Buer's father. not very original with the names, in fact all branches of the family only seemed to use four names either William, George, Charles or Henry making untangling them pretty confusing.
Regards
Max