This is very sad. I am a bit confused about the location though. If the helicopter was going from Redhill to Elstree I'd have expected him to route Banstead to Barnes and then try to go north. In that area he'd be talking to Heathrow but it is to the west of Battersea and Vauxhall is to the east, beyond the heliport. Given that the crash site is south of the impact with the crane I wonder whether he'd decided to divert and turned right along the river, realised he'd missed the heliport and done a turnback across the river - all the while being to busy to change frequency to Battersea.
As already mentioned the Heathrow trace is very acuurate (I have also been reminded of my ever so slight divergence from the approved route) so they will no doubt be able to provide something. As an aside, the maximum permitted altitude on the London QNH along the river to the west of Battersea Heliport is 1000', to the east as far as Chelsea Bridge it's 1500', as near as damn it agl heights. The helilanes rules state that helicopters must not fly below 500' separation and I think it's a 1km minimum visibility, but pilots must endeavor to fly at the maximum altitude for the sector.