Originally Posted by
Calchas
LHR cannot entertain you for eleven hours.
If you can entertain yourself for that long, find a quiet spot in a lounge. Otherwise, go to Windsor or London. Many museums in the UK are free to enter, particularly in London, and public transport from T5 to South Kensington is, as Microwave suggests, cheap, safe and easy.
Heathrow discourages entering into the wrong terminal. It is possible [except T5] if you are insistent but staff will assume that you are lost. You may also be denied lounge access except in the departure terminal.
Indeed, it is a policy of the airport authority that airside lounges (other than arrivals and any possible landside locations) are strictly departure lounges for passengers departing from the terminal the lounge is situated in. There are ways to do this anyway, but they are tedious and generally unproductive considering the alternatives and generally better lounges at T-5.
I'm also thinking the Elemis spa courtesy treatments may be restricted to longhaul BA First passengers and BAEC Gold members? I suppose treatments may also be available for fees, arranged upon arrival at Terminal 5A South lounge, Terminal 5B departure lounge or Terminal 5 Arrivals lounge. (And for the return, Terminal 3 BA Galleries departures lounge as well.
The OP will be required to exit T-3 either landside via HM Immigration and Customs or to T-5 via the Flight Connections channel, with no opportunity to use any T-3 lounges outbound to VCE.
I'd certainly check my baggage through and heed the excellent advice given by
Microwave, picking up some GBP at a T-3 arrivals hall cash machine and heading out of Heathrow for a few hours, unless some condition precludes that.