T.W Postern Gate

I wonder when Postern Gate became the one word Posterngate in use these days. No matter, it is of no importance. The mysterious T.W I've heard stands for Trinity Ward a reference to the Trinity House mob who ruled the area back in the day or perhaps (and more likely) that Holy Trinity Church is just across the street. I'm sure I've shown a bit of this building before ... ah yes here it is.