I would not hesitate to coming down the day before. You have a plethora of hotels at Heathrow in which to stay. Indeed, what we have done in the past is stay at the Hounslow Travelodge. It is quite close to Hounslow Central tube station and a room there mid-June on Flexi rate is about £87. It is never going to be admitted to Relais and Chateaux but it is perfectly fine and far enough away to be better than a Heathrow Flophouse like the Thistle or ludicrously expensive like the Sofitel. I would add that down the road from the Travelodge Hounslow there are some fairly decent places for dinner. We ate at an Italian place that i liked - there are plenty of others. Heathrow has only one place that I would return to with pleasure and that is The White Horse. Just my 2p worth.