According to this, he was apparently a member of the Bedford Head Covent Garden Lodge, and of the Maid's Head Lodge at Norwich (and not, apparently, the White Swan, as I wrote previously).
However, the Bedford Head Covent Garden Lodge doesn't have a number. And nor does a search for the Maid's Head Lodge at Norwich turn up a number (although it should be borne in mind that the situation with some of these early Lodges was sometimes very confused) - and despite the fact that there is a present day Maid's Head Lodge in Norwich (no. 8558).
At this point, I think it would be much simpler if either Scott or Gary could kindly supply their source for "London Lodge no. 78". Is this the Bedford Head Covent Garden Lodge, or some other one?