United Kingdom

Three hours in town against the cost of a car in both directions is thin on its own. It only stacks up if you were going to pay for a day room anyway, and then the numbers get close enough that you stop arguing about it. Also Heathrow to Westminster at nine in the morning is not an hour. Budget ninety minutes and be pleased if it is less. Pick one place and stay in it.

I planned exactly this for a Heathrow stop in February and I made a spreadsheet for it, which tells you what you need to know about me. The e-gates are under ten minutes when the terminal is empty. A 7:20 arrival is not empty. Mine landed with four other long haul and I stood 35 minutes. So half eight is optimistic, nine is realistic. For the nap I would turn it around. Let him sleep in the car going in and arrive at eleven with the sleeping already done behind you. And if you stay instead, in Terminal 5 on the upper level past the pharmacy there is a stretch of seating where almost nobody sits. The baby change there was clean at six in the morning. I did not need it and I noticed it anyway, this is how my brain works.