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I’ve only done that bit of the A4 by bike once when I went right through to the east end. I had a funeral to get to in Tower Hamlets and there was a train strike on. Early-ish on a Sunday morning and it wasn’t too bad until a couple of miles before Hammersmith tbh, but I wouldn’t do it at any busy time. I came back the slightly longer way through Richmond and Twickenham because the roads are way nicer.
Apart from the slight kink on your map at Stanwell where I went straight on, that is pretty much the route I took. The road network over that way is as @mespilus described. There’s not really much out there except depots and support industries for Heathrow, probably why there are no small roads.
That bit of road mespilus described where where the underlying concrete slabs have moved was pretty dreadful. Luckily it was fairly quiet.