Is there a 12-hour daytime layover possible? That gives you enough time to get into London to see a few things. But a 7-hour layover does not. Add up an hour to get through immigration/passport control, an hour each way on the tube ( which will be extremely crowded if your travel is during morning or evening rush hour, and three hours for security, etc. before a long-haul flight, and you have nothing left.
We travel through Heathrow on BA miles on every trip. If I cannot get a 3-4 hour layover time, I just book as far as Heathrow with the miles, and pay for the shorthaul segments separately. We spend at least one or two nights near Heathrow in each direction, and always enjoy our time there. Once we overnighted in Windsor, and on another trip it was two nights at Henley-on-Thames. Or we go into London by Heathrow Express and stay near Paddington, enjoying a long walk in Hyde Park the next morning before heading to the airport.
Once we were traveling onward from London by train to Paris, so we only wanted to go as far as London anyway. In every case we have gained more flexibility this way---often I do not have a firm itinerary in mind when I book the two Business Class seats the day they are released, 355 days in advance, so it is nice to know I can figure out the rest later.
