Hi Sarah I may be able to help with your Ransley enquiry.
I am a Ransley descendant as well and I know a couple of people who have done a lot of research into this name especially in the Kent area.
William and Thomas are used quite a lot and London is a large area to search.Was there a mother's maiden name on the birth certificate for Thomas?There was a marriage in Kent in 1837 of a William Ransley and Betsey Barfoot and William's sister married a few years later in London.
However I have no evidence of William and Betsey after 1837 so would need some confirmation that this is the same couple.If you have a specific address on the birth certificate it may be possible to check the 1841 census but this would only show the county of origin, not the place.
Do let me know if you have any further details and I will put you in touch with a Ransley expert!