I can’t offer any concrete facts but the available records certainly give room for theories!
I noticed that on the 1851 census Daniel THOMAS is shown as a visitor but there’s no sign of his children so I did some hunting and found this census record:
Middlesex>St Giles in The Fields>St Giles South>District 6>52
Address: 10 Little Wild Street (the same as given on the children’s baptism entries)
L THOMAS Head 50 b.1801 Berkshire
Amelia THOMAS Dau 12 1839 Clerkenwell
Albert THOMAS Son 6 1845 Smithfield
William THOMAS son 9 1842 Smithfield
Edmund THOMAS son 2 1849 Smithfield
I think the L has been mistranscribed and should be an S. If this form was filled in by Sarah Cooper (who I can find no trace of on the 1851 census) it would explain the slightly out dates/birth places. The occupation of the head appears to read ‘Broken man’ – no, I kid you not, although it could read ‘Broker man’ but that has no connection to his real occupation.
If this is the right family where is Daniel’s wife, Harriet? I saw that you have her death in 1853 St George, Hanover Square, so I went hunting again and found a Harriet THOMAS mar 54 b.1797 Sevenoaks Kent as a visitor at the home of James J CHALK (barrister not in practice), at 80 Warwick Street, St George Hanover Square. I know the date & place of birth don’t match but I can’t find this woman either on the previous or next census. Might be interesting to see whether the address given on your Harriet’s death certificate matches this one.
I’d make a guess that Edmund’s real mother was Sarah COOPER as recorded on his birth certificate. As for the different name on the baptism record, I’d put that down to the fact that all the children were baptised together and the older ones would have certainly known the name of their real mother, so rather than having to confess to the vicar that the youngest one was born out of wedlock it would have been simpler just to put the same name on Edmund’s baptism record.
Food for thought, but it’s just my theory, of course.