"Theo" wrote

Woking-Clapham Junction
Clapham Junction-Feltham
285 bus to LHR

is the most obvious alternative, though somewhat slow.

Guildford-Worcester Park
X26 bus to LHR

is one I haven't tried.

I suspect if the M25 is borked then Woking to Heathrow is going to be
difficult whatever. Staying on the train and getting off a Surbiton (if it
stops) then taking a taxi might be one way to avoid it.

Bus (any) Surbiton to Kingston then X26 to LHR is workable.

Rail via Weybridge to Egham or Staines then, eg 441 bus works but Feltham is
faster.

--
Mike D