Travelling to London is pretty much the same as it was before. Masks are "mandated" but no one has ever enforced it, you can claim to be exempt without having to provide a shred of evidence and therefore I'd say a good half of people I encounter on my public transport journeys are unmasked, use them as chinstraps or have noses sticking out.

If you're using the Tube to travel into London, be aware that services might be even less frequent than before Covid. By my reckoning a good quarter of the trains that used to run to LHR now stop, for reasons that fail me, at Hatton X. I'd rather use the LHR Express or, the new TfL rail (former Heathrow connect, soon to be part of Crossrail). It's actually a civilised way to travel, the trains are huge, it's faster than Piccadilly to get downtown and it doesn't cost an arm and a leg like LHR Express.

Regarding cars, there's now the option of picking up a Zipcar from the terminal and I had a weird experience a few days ago with a Bolt pick-up where the driver wanted me to wait outside as he couldn't stop to pick me up. Don't know why. Traffic on the M4/A4 is back to normal and the M25 is not far behind.