Hi
There is no question on the marriage certificate which specifies whether a father was dead or not. It was the custom and practice of some officials to ask the question and note it down. Many did not, though more did as the the century wore on. It was the custom and practice of some officials if the information was supplied (even if it wasn't asked for) to note it down. Again many did not. Churches in London were often marrying quite a number of people on anyone day, so they wouldn't spend a lot of time on the details before moving onto the next couple. Elizabeth may have supplied the information because her father would not be present to 'give her away'.
By 1860 nearly all churchyards in central London had shut and burials were in civic cemeteries that had consecrated ground - for Anglicans and non-consecrated ground for others. With a death registered in St George Hanover Square - Westminster, the first cemeteries to check would be Westminster ones. Westminster cemeteries because of space were established outside the borough.
Checking most of the civic cemeteries in London would be a mammoth task - there are over 150 of them, though not all of these would have been open in 1860.
Westminster cemeteries
Hanwell cemetery opened in 1854 and East Finchley opened in 1855. Paddington opened in 1855. If he was buried by the poor law guardians then some Westminster poor law unions had a deal with Brookwood Cemetery in Woking Surrey which opened in 1854. There was a train service with its own special platform which went straight to the cemetery.
Westminster council hold the records for Hanwell and East Finchley. Westminster controversially sold all its cemeteries in 1987 for 15 pence. These two cemeteries were neglected and following a public outcry Westminster was forced to buy them back. Paddington cemetery had been sold to Brent council however and they still maintain it.
Westminster cemetery office
http://www.westminster.gov.uk/services/communityandliving/burials/Westminster Archives guide to cemetery registers
http://www.westminster.gov.uk/workspace/assets/publications/Info-Sheet-07-Cemetery-Regs-1278423620.pdfBrookwood cemetery registers are held on microfilm at Surrey History Centre.
Brookwood cemetery
http://www.brookwoodcemetery.com/Finding James or his brothers' burials will not help with establishing further information on their parents.
If Thomas senior, his father, died before the 1841 census it is more likely he was buried in a churchyard, though Kensal Green cemetery opened in 1833.
Regards
Valda