Roland Perry wrote:

It's actually quite difficult to get from the A40/M40 to Reading (I used
to live quite close to the M40, north of Reading). The road is diverging
to the north quite significantly. I suppose you could try going via High
Wycombe and Maidenhead Thicket (as long as the M4 was OK west of there).
But it's an awful long way round.

M40, A404 and then A4 or A4155 according to your pick. Given the
circumstances, A4155 may be better option.

M3 J3 and Bracknell is a better alternate (and it's further away from
the influence of the original jam).

I know all the routes to Bracknell. Worked there once. From Heathrow
you could even just go onto the A30 then A329 through Ascot. Of course
that route may also be full of A4-avoiding traffic.

If you're starting at Heathrow T4 then you're already on the A30. If
not then you can head round the ringroad.