There's no need to carry photo ID. Don't encourage them, we're not in a Police state just yet. I never carry it, and having had a stern lecture from a gun toting PC Plod at LCY that I ought to carry my passport around with me in my own country, I now make a point not to carry any photo ID at all.
You'll be very unlucky to meet the Police on a weekend anyway. They can't afford the overtime.
My bank cards all have the same name so that always does the trick.
A car is worse than useless at Heathrow, all the spots are walkable using the Piccadilly Line from T5, T4 or Hatton Cross. There is also a good spot on the Southern Perimeter road when departing 27L that is good for heavy departures. It alsa has a handy petrol station for bathrooom breaks and food. Again walkable from T5 or more easily T4.