This is cheeky... but it works a treat...
The Park Inn is right next to the NCP Flightpath car park. (Walk out of reception, turn right over the bridge - max: 3 mins walk). From there, there is a free shuttle bus to Terminals 1, 2, 3 that runs every 15 minutes. They do not ask for any ID to show you have parked there.
Free transfers from the Park Inn to LHR