7 hour layover in LHR - enough time to visit London for a couple of hours?

Definitely, more than 2 hours. I actually have such a connection quite regularly, and always spend some time in the city. Wouldn't go to museums and such though, but enough for some general site-seeing and even maybe some shopping on Oxford Street. You could probably squeeze in a whole round-trip on the tour buses they have there, without getting out anywhere.

You can go to see the Windsor castle in that time or spend 3-4 hours in London, and have enough time to watch the airplanes taking off from the terminal while you're waiting for boarding.

The express train takes ~20 minutes to Paddington, and from there you can take the tube - 5-10 minutes to virtually anywhere interesting.

Going through security is pretty fast, they have like 20 lanes there, and it never takes me more than 10 minutes to get past that. Accommodate some spare time, but generally they're pretty efficient. Be at the airport at least 1 hour before the boarding starts.

You can expect some delays at the immigration (on arrival, unless you're a EU citizen), and waiting for the train in each direction, check the timetable.

On the getting back side, from the BA website:

• You must pass through check-in no later than 45 minutes before your flight (Means get your boarding pass, have your passport checked etc)
• You must have entered Security at least 35 minutes before your flight departs. (The bit where they scan your boarding pass, before the xray stuff)
• You must be at your boarding gate at least 20 minutes before your flight departs (For B/C gates this means you have to wait for the little train, get out there etc. For A bus gates, it's to the wait for the bus)

So, if your bags are checked through and you already have your boarding pass, and you don't mind cutting it close, you could theoretically not need to leave Paddington again until gone 5.30pm! However, ~6pm can be a little busy, so allowing the minimum 35 minutes might be a bit tight to get to the B and C gates.

If you're an EU citizen and you get lucky, with a 12pm arrival you could theoretically be in Paddington just before 1pm if you take the Heathrow Express, or the west end by a little after 1.30pm if you take the tube. If you're not an EU citizen, and you've arrived at a busy time, it may take longer...

So the other answers have focused on intra-terminal time. I'll point out that once you take that into account, you'll have what, 3-4 hours outside the terminal, to be safe.

We can improve this by getting you to checkin BEFORE you leave the terminal. So exit immigration, go around to your departures terminal and check in - luggage if you have any, and so on. Then head off. Worst case you'll lose your flight and they'll chuck your luggage off the plane, right? ;)

Now you COULD take the express to Paddington and then as you say, anything is close. You could also do something outside London.

For example, Kew Gardens is reachable by tube, and you could spend a couple of hours there if the weather is nice.

But otherwise, from Paddington it's 30 minutes to Wimbledon tennis stadium if you'd like to see something else outside central London - but beware, one tube stoppage and you may be struggling to get back.

Odds are you're safer doing something in central London, as you then have several speedy-ish options for getting back to Heathrow.

Make sure to pick up an Oyster card either at Heathrow or at Paddington, as it'll make your tube journeys less expensive.

You can also buy an Express train ticket online, which I gather saves you some money over buying it on the train. And get a return, again saving you some time.

There's also bag storage at Heathrow, but if you checkin before you go, you won't have to worry about your bags, and it'll save you time and money :)

You've just about enough time to get into London for a couple of hours. However, it will be easier, as you're a tourist, to catch the Piccadilly line tube from Heathrow itself. That means no waiting for trains (the express is real quick but you will have to wait for it and you'll have to get to Paddington to get it and it requires you to change tubes) and no changing.

So I'd suggest to limit yourself to seeing stuff that is going to be near this line. The oyster card you have to pay a deposit for, but with this plan you just need a return tube ticket (and not a travelcard/OYSTER).

p.s. Green park is right next to Buckingham Palace.