6 hours layover in London Airport - Visit London City too

Given six or more hours between arrival and departure at London, it is possible to make a quick trip into London City. This should easily give around 90 minutes of time in London, assuming 1 hr of travel time from the Airport to Piccadilly Circus.

There are caveats - sometimes, the tube and/or security at London can be a long drawn out affair. But having just made this quick run, I ended up with 45 minutes to spare at London for my departure, so it was all quite comfortable.

Of course, all I did at Piccadilly Circus is walk around a few blocks, basically just exploring streets, shops, and small parks. And the tube ride itself was a novelty. All this activity is much more fun than lounging around at Heathrow!

So here's how it all worked out: Arrived at Heathrow at 9AM. Felt awake and good, so decided to try out a trip to the City. Immigration was quick, under 5 minutes. Note that some passengers are not allowed out of Heathrow - so be sure to check your transit status.
9:30AM was at the Underground station. There is also a faster Heathrow Express, but it is far more expensive, and not really worth it to get to Piccadilly Circus since it requires changing trains at Paddington. Best to just stick to the more frequent tube, and sit in one place for the entire journey.
Tube tickets: Zone 1 to Zone 6 travel ticket is what you need to get to the city from the airport. Unless you have a Oyster travel card, for off-peak travel, best to just buy a 1-day travelcard. Off-peak is valid if you start and end all travel between 9:30AM-4:00PM. Peak and off-peak times ticket prices vary a lot. And they have a complicated pricing system - paying in cash for single tickets is quite expensive, which is why a travelcard turns out to be decent deal. In Feb 2013, for travel between Zones 1 and 6, £5.50 was a one-way anytime ticket price, and £8.90 was the off-peak 1-day Travelcard. If you plan to visit London often, pay the one time £5 fee/deposit for the Oyster Card, which then reduces the one-way off-peak ticket down to £3. All very complicated, so usually easiest to just stick to two one-way tickets for peak-travel, and one 1-day travel card for off-peak travel.

So, with ticket in hand, take the subway, with the train going to Cockfosters, and get off at Piccadilly Circus.
There can be long delays on the tube sometimes, but in the few times I've used it, never more than a few minutes of delays.

At 10:30PM, I had reached Piccadilly Circus! Nice day in London too, sun was out, restaurants were buzzing, and there was even a movie shot going on around the inside streets.

At 12noon, got back in the station, and took the train to Terminal 3. Within an hour was at Heathrow, and security was a breeze too, so ended up having 45 minutes to spare before they called the gate for my flight. They announced the gate at 1:45PM from my 3PM flight time. It does take up to 30 minutes to walk from Security to the Gate at Heathrow, it is a huge sprawling airport.

All in all, a very comfortable and easy trip out of Heathrow and back to Heathrow.