According to the FamilySearch website, only about 30% of London parish records pre-date 1620, but many of them will have been lost for other reasons than the Great Fire.
I don't think you can be sure that William Trueblood, baker of London, was from an established London family solely on the basis of there being no matching entry in the Lincolnshire records. Pre-1660 records for all of England are very incomplete.
I've only skim-read the will of William Trueblood of St Giles Cripplegate of 1665, but it refers to a wife, Anna nee Harding, several children (who seem to be under-age) including John, and a sister Olive. There is an Olive Trueblod daughter of John baptised in 1627 in Barnby in the Willows, Nottinghamshire, which is close to the Lincolnshire boundary. Do those names or places feature elsewhere in your tree?