I looked at the London Marriage records myself.
Definitely says father William, a Carman.
Just a thought - Thomas didn't die until 1895:
Deaths, December qtr 1895
Croydon district, vol 2a, page 133
Toomer, Thomas
So where was he in 1891?
Maybe Walter's father really was William?!

And Thomas upped and left the family?
So it's the birth certificate that could be telling.