This Brutus chap who turns up in London folklore is not the one from Shakespeare's Julius Caesar, but a supposed survivor from the sacked city of Troy. Have a look at "Brutus of Troy" on good old wikipedia for an excellent summary. The notion that a handful of Trojans would leg it all the way across Europe to settle down anew in misbegotten and backward Britain is probably a little far-fetched. There probably was a Troy (there is a corresponding archaeological site at Hisarlik in Turkey) and it may well have been sacked by a load of dudes from Mycenae about 1200BC, but there is no Brutus or similar name in the Iliad, which was written down from oral history about 800BC. So all in all a load of old cobblers? Not entirely as there have been waves of invasions from the continent, notably the Roman colonisers, and one feature of colonised literature is that old native stories are given a flavour of the occupying culture as a way of making them seem more respectable, a little like building a church in the middle of Knowlton Rings. Old stories about legendary king Bran/Bendigeidfran sounded much better in the early middle ages once they had been given that Latinate gloss. I find it easy to believe there was a native hunting ritual that took place here, which was assimilated and survived in some form until the 1500s, given a respectable "Diana" label. Corresponding Christian saints would be Hubert or Eustace (both symbolised by a stag's head with a cross between the antlers, which will sound familiar to those of you who have read Riddley Walker), but I'm not aware of any old City churches dedicated to them geezers. Anyone up for a re-enactment?
Further to RiotGibbon's post, I found this in Peter Ackroyd's "London the Biography":
In the records of St Paul's Cathedral the adjacent buildings are known as 'Camera Dianae'. A 15th century chronicler recalled a time when 'London worships Diana'. She was the goddess of the hunt, so perhaps linking with the ceremony "that took place at St Paul's as late as the 16th century: a stag's head was impaled on a spear and carried about the church; it was then received upon the steps of the church by priests wearing garlands of flowers upon their heads."
The Temple was allegedly built by Brutus. Diana (the Hunter) appeared to him in Malta about 1000BC, speaking of the "Great White Island". Landing in Totnes, Devon, he came to London and built a temple to Diana/Herne. This lasted until about 700CE, when the first St Pauls was built.