Thanks for the replies avm228,
The daughter does seem to be Mary's child before she married Thomas Simmonds Cook, she also had an earlier daughter, Jemima, who didn't survive childhood. As for the little boy, the fact that he was born in Marden rather threw me off track and the fact that he was listed as Mary's grandson in a later census record. I actually found a Thomas Simmons born in Marden to an un-married mother in 1851, so put two and two together and made five!
As to finding Thomas Simmonds Cook in 1841, there are several Thomas Cooks around Sussex and,not being familiar with the county, I was really unsure if any of the locations were feasible. The other thing is, as already mentioned, why would the name of Cook be dropped by the widow? It doesn't make sense.
I have found several christenings for Thomas Cook in Sussex, but, again, I don't know if the locations would be right for someone born in Lindfield.
Mary's great uncle, Thomas Hope, was also living in Boughton Monchelsea in the 1840's and his wife was a Simmons, though her family were the Day's from Marden, so things do get a bit tangled at times.
There were many families around the Weald of Kent by the name of Simmonds, Simmons, Simons, and Symonds and sorting them out can be a nightmare, but I haven't as yet come across any who came over the county line from Sussex apart from this Thomas Simmonds Cook, so whether his family was connected to the Kent ones or not is something I would like to find out if possible.
Anyway, thanks for your help with the children, I will get the birth certificates.