Recommended wheelchair accessible transport from Heathrow Terminal 4 to London and around London?

The Elizabeth line is wheelchair accessible. https://tfl.gov.uk/travel-information/improvements-and-projects/improving-accessibility

Any bus in the UK now has to be what is called Diptac compliant (Disabled Persons Transport Advisory Committee) [sorry about the use of the pejorative word Disabled, when differently abled would be better).

As such there will always be at least one wheelchair space. Of course this will be downstairs so you will not get the real benefit of a HoHo- being upstairs. But if your friend is actually wheelchair bound (rather than being able to walk a short distance, but otherwise needing the chair for overall mobility) that is probably the best you will achieve.
As part of DipTac the buses have to have a ramp for smooth boarding from the kerb/sidewalk.

Buses will be a lot easier to use than the tube which is still largely inaccessible. Wheelchair users have priority for the accessible spaces on buses, so in theory people with prams and strollers should get off to allow access.

The traditional London black cabs are also all wheelchair accessible with a ramp like the buses have.

if you are using the covered walkway - I prefer to think of it as an above ground tunnel - between the 4 hotels attached to the side of Terminal 4 (Premier Inn most distant, then Hilton, then Crowne Plaza and Holiday Inn Express share one route off the tunnel and share a building, then it is still some distance) be advised that there are some bumpy floor joins and slightly narrower bits of that tunnel. My wife is disabled and uses a walking device and noted - yesterday - some of the difficulties. Probably easier in a wheelchair if it is designed for outdoor use. Still a fair walk though.

There are also buses linking the terminals with stops near the hotels.

Both the Elizabeth Line and the Underground can be accessed from Terminal 4. Elevators (lifts) are available between levels. The Elizabeth Line seemed closer to the hotels at terminal 4 than the underground, but both are accessible.

The underground often stops and waits for about 8 minutes before continuing on to Terminal 2 and then onto Central London. You might find that you appreciate having those few extra moments to get settled.

I am not a big fan of hop on hop off in London, but perhaps you are choosing this due to Mobility concerns.

Thank you all for this helpful advice. Is there a preference between the Elizabeth line or the Underground?

And, in response to thoughts about HO HO busses, we like them to start in a city for an overview. You can study maps, but SEEING helps it all make sense.

Many thanks, Ginny

The preference between Elizabeth Line and the Tube really depends on which of the many possible locations you intend to pick the HoHo bus up at.

On the TfL journey planner- https://tfl.gov.uk/plan-a-journey/ enter your planned journey then at the foot of the results page choose 'full step free access', on the next page click 'access, lifts and escalators' for any further information- for instance the current lift problem stopping step free access to several of the tube lines unless you request special assistance.