flanner's idea is definitely doable, since the Library is only a few steps from the station. It would still be rushed but you could have 45 mins or so at the British Library - depending on whether 'stuff' happens or not. If you are delayed at all at LHR you can just take the National Express coach straight to LGW. If you land early or don't face long lines at LHR you can squeeze in some time at the Library.

Alternatively just go as far as South Kensington - 3 major museums within 5 minutes walk and only 40 minutes from Heathrow by Tube.

Alan,

That's an excellent idea. Here's the Victoria and Albert policy on checking bags, as you have carry-ons they will let you check them:

http://www.vam.ac.uk/content/visit-us/facilities/

Victoria Station is just two stops on the District Line from South Kensington or a short taxi ride.

Good idea -- still only 45 mins to an hour 'top side'.

I've checked shopping bags as large as a carry on at the V&A

Depending on how light you are travelling, at the British Musem cloakroom:

"The main cloakroom is to the west of the Main entrance. £1.50 per item, 50 pence for umbrellas, fold-up pushchairs free.

Maximum size: 40x40x50cm
Maximum weight: 8kg

Thank you for the great suggestions. We are travelling light, so leaving the luggage at the Museum would not be a problem. Since we don't have to wait for luggage I'm hoping that we can get to KX and then take a taxi to the British Museum by 10 am. If there are long lines at Immigration and we see that the future is kind of bleak we'll either take the tube to South Kensington, or just make our way to Gatwick. We'll just have to play this by ear. Thank you so much for your help these are great suggestions, I hadn't thought of the Victoria & Albert museum.

I thought I should let you all know what I finally did upon arrival in Heathrow. We were fortunate to get out of the airport by 9 am, and we took the tube to KX, we walked to the Museum, and got there by 10:20'ish, we were able to leave the luggage in their cloak room, but we had to take stuff out of our suitcases because they have a scale on their desk and if it weighs anymore than 8 kg. you have to put the stuff in baskets and check in the baskets. All in all it cost us 5.50 to check in the luggage. I was interested in seeing the Rosetta stone, and we couldn't even get close as there were people all around about 6 or 7 deep, we saw a couple of more things but we were ready to leave by 12 noon. We went to the Tavern accross the street and had a lovely lunch then we took a taxi to take us to the train to take us to Gatwick and got there in plenty of time since we had boarding passes. All your input was very helpful. Thank you so much. It was much better than staying for 8 hours at the airport.

I am glad it worked out so well for you!