The questions are, Where was he born? and what name was he registered with?. If he was born 9 Dec. 1875 then he should have been registered in either the Dec. Quarter 1875 or possibly the Mar.Q.1876.
Was he a son of George? George married Lucy in the Dec. Q 1875, they lived near George's parents (and George Junior), so if he was George's (or Thomas George) father, surely George junior would have known and given his name at his wedding.
I think that he must be a son of Hannah. Hannah was living in London by 1871, she had plenty of opportunity to have a liason with a Thomas Lovett. So where did the birth take place, London or Suffolk and in what name was he registered?
If parents were not married it was usual to register the child in the mother's name. The only Oastler in that period was a Charles Oastler, St Olave, Dec.1875, 1d, 270, so that must be a possible, but why Charles?. There are a few Ostlers but nothing that stands out in London or Suffolk.
I can see that his birth is given as Tannington in 1881 and you say he was baptised in Brundish. Both parishes are in the Hoxne district but there are no obvious registrations there. In fact there were no registration in Hoxne for a Thomas and only 9 Georges, none with a surname that sounds familiar. The only registration in Suffolk that I think could fit is of a George Lovett, Plomesgate, Dec.1875, 4a, 672. It is possible that Hannah returned to Suffolk for the birth but did not quite go home to avoid family embarrassment. If this is him then I would assume that Thomas Lovett came too and they posed as a married couple for the registration.
What happened to Hannah? Was it her that married in Lewisham June 1880, in which case her relationship with Lovett did not last.
You may have to purchase possible certificates in the hope that you get the correct one.