I don't have a candidate for your Thomas (although from a negative point of view that means I'm pretty sure he's not one of the Bedfordshire Meppershall/Arlesey branch of Rainbows), but have you thought of trying the archives of the Goldsmiths' Company (see
http://www.thegoldsmiths.co.uk/thelibrary/archives.htm)? If your Thomas was a silversmith in London then he ought to show up in their records, and if silversmithing was the family trade then you may be able to get back several more generations through their records.