Had a good read and this is what I've found. We'd like to keep our William as we don't think he faked his own death and burial in 1890!
How about this lot
1841 HO107/1075/4/39 Seething Wells, Kingston, Surrey
Bradley James labourer 30 y
Mary 30 n
Thomas 8 y
William 5 n
Charles 4 y
James 1 y
1861 RG9/773/14a Lampton, Heston, Middlesex
Bradbury James Head M 51 brickmaker Egham Surrey
Mary Wife M 50 Middlesex
William son U 25 labourer brickfields Egham Surrey
James ? U 21 labourer brickfields Egham Surrey
Mary Ann dau U 17 Middlesex
1871 RG10/1312/166a Isleworth
James & Mary
1871 RG10/1312/99a Isleworth
William, wife Charlotte and children Martha8, William5 and Eliza4
1861 Jun Brentford 3a 72b BRADBURY William / BAILEY Caroline Charlotte
1881 RG11/1340/64b Hounslow
James
1881 RG11/1340/61a 1901 RG13/1185/153a
Charlotte & Eliza
Charlotte dies in 1907 Mar Brentford 3a 54 BRADBURY Charlotte (73)
and there are all the other family members in and around the area. Do you like this William?
Hope it helps
Chris