Maybe staying in one of those ever so expensive hotels near Heathrow is the only answer!!
I appreciate everyone's budget is different but I've heard similar comment made recently and again would point out that it is perfectly possible to get a decent hotel room around LHR for under £50, but you need to look beyond the supposedly (!) upmarket brands on the hotel strip on the Bath Road.
I've just done a quick dummy booking at a well known hotel chain which has several hotels around the LHR perimeter and at one their brand new very accessible hotels, very very handy for Heathrow there are double rooms available for under £50 a night if you book about two weeks ahead.
( just to emphasise that the hotel I checked is not some remote hotel out at Slough or beyond Colnbrook, it's a big hotel on the perimeter road and is 5 - 10 minutes sheltered
walk from one of the Terminals.......)