10 hour layover in London

Here is the cheapest way to see a bit of central London. Buy a one-day zone 1-6 travelcard at Heathrow. Take the tube (Piccadilly line) to Hammersmith, walk across the platform, and change to the District line. Take it to Westminster. You'll emerge right across the street from Big Ben and Parliament. Go for a walk to Trafalgar Square. Take the tube back to Heathrow. Allow one hour each way.

Go here to print a tube map and a central London bus map that shows the location of major tourist attractions, including several that you'll pass by on your walk.

That's a great idea! You'll also see the London Eye (look left across the river when you get out of the tube at Westminster), Westminster Abbey and on White Hall there's the Horse Guards and No 10 Downing Street. Covent Garden is not that far from Trafalgar Square, easily walkable in 10 minutes, go check out the markets and from there (Covent Garden station) you can take the Piccadilly Line straight back to the airport.

Covent Garden

Map

FYI. You can also get a HEX Visitor return ticket (Heathrow Express) for £17 per adult. The HEX takes 15 minutes to get into central London as opposed to 45-60 minutes on the Tube. The HEX will get you to Paddington Station, but if you intend on getting the Tube/Public Bus for onward travel, you'll either need a PAYG Oyster Card or a Travel Card which'll set you back about £5. Rather than getting the tube around, I'd suggest walking outside Paddington Station and getting a ticket for the one of the hop-on and hop-off tour companies, they'll give you a good above ground tour of central London and you can hop-on and hop-off all day.

The only catch with the HEX visitor ticket is "Visit London tickets are valid after 13:00 (returning before midnight on same day of travel)".

Of course your visit all depends on what time of day you're arriving...

Cheers