Heathrow to British Museum

This www.heathrow.com/transport-and-directions/getting-to-central-london gives you all the information you need.
The tube (Piccadilly Line) is best: the Russell Square station is almost on the doorsteps of the British Museum.

Heathrow to Russell Square (for the British Museum) takes one hour by Tube.

Don't forget to factor in the time it will take to get off the plane and pass the UK border (say an hour), and the time needed to return to Heathrow (another hour), plus you're advised to arrive at Heathrow three hours before a flight.

So that's six hours before you've even stepped inside the museum.

If you have such a long layover, you will have to collect your bags and leave them at left luggage, which is costly and time consuming. You will need a minimum of 6/6.5 hours plus however long you need at the museum. You may want to make allowances for late arrival too.

"I am trying to schedule the flights so that we have a long layover at Heathrow."
Since you are still in the process of booking your flights, consider giving yourself one night in London. Consider flying into Heathrow, staying at an airport area hotel. That will give you the entire afternoon of your arrival to go in and see the items of interest at the British Museum, plus walk around London that evening. Tube or train back out to Heathrow, sleep at your hotel, depart the next day. That gives you time to enjoy the Elgin Marbles, and a stopover in London, without rushing.

Too bad you can't make this London stop before Greece, so you could return the "Elgin" Marbles to Athens where they belong! ;-)

I also concur with staying the night (or two) in London versus trying to fit London into a layover. First of all, if you're flying back to North America from Greece through London, you probably won't have enough time anyway. I think the latest flight out of London for the USA leaves late afternoon...

I would, however, recommend staying at a hotel just outside Paddington. There are plenty of reasonably priced hotels within walking distance to Paddington Station and you'll have great tube and bus connections to the rest of the city as well as easy and fast travel back to Heathrow.