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@matt_r_p
There is - incredibly - separate cycle lane provision along the A4 just about all the way from Chiswick Roundabout (ie junction of A4 and Gunnersbury Ave / A406) to Heathrow.
So I would suggest getting to Hammersmith roundabout (which presumably you know how to do) and then taking King St / Chiswick High Rd to the roundabout. Hammersmith to Heathrow should take about 40-45 mins. Hope that helps.