From San Francisco to the UK the great circle track is over NW Nevada, Idaho, Montana, Manitoba, Hudson Bay, southern end of Baffin Island, southern Greenland, a little way South of Iceland, the Hebrides, Glasgow, Lake District and into Heathrow via Bovingdon, NW of the airport. Thence if you're landing towards the West at Heathrow yes it would be over central London on the way in, and very scenic too on a nice day.
HOWEVER!! The route flown between two cities on a long-haul network varies enormously from day to day, and we will go a long way off the great circle track (shortest distance) to take advantage of the best tailwinds or avoid the worst headwinds: What we are after is minimum time, not minimum distance. On the way back from California to Heathrow I have been as far South as New Mexico, Texas and New York in pursuit of the shortest time. Incidentally the number-crunching to find out how far off the great circle it is worthwhile going to find better winds is done in most airlines by a flight-planning department and a big computer.