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What is the best (mix of cost effectiveness + speed) way of getting to London's various airports?

I'm an American that will be staying extremely close to St Pancras station for a couple weeks. It would be nice if there was a convenient way of getting to the various airports so I could take day trips to other cities in the UK. I see I can buy tickets online to get from St Pancras to basically every airport, but I'm not sure if it's the best way. Most do look pretty affordable, but I'm unfamiliar with the speed and reliability of the trains.

For example, I've been to Japan several times and they have a rail pass for visitors that works on the largest rail system (JR). I doubt London has any equivalent, but maybe? Or maybe there are day passes for use on certain trains that could get to me the various airports?

Generally, you should check e.g. maps.google.com for travel times - the choice between road and train for getting to the London airports can depend on time of day.

An Oyster card gives you good fares on the local Transport For London services.

I strongly recommend train rather than air for inter-city travel in the UK, except possibly for the very longest distances, and for crossing to Northern Ireland.

For example, consider York. Virgin Trains East Coast has a once every half hour direct service from Kings Cross, which is adjacent to St. Pancras. The faster trains are under two hours, the slower ones under two and a quarter hours. Walk out of York railway station, and you will see the city wall and be within walking distance of e.g. York Minster.

The actual flight time from Heathrow Airport to Bradford Airport, the closest one to York, is shorter, just over an hour. However, by the time you have traveled out to Heathrow, allowed for security and check in time, and got from Bradford to York it would take several hours.

London to York by car would take between three and a half and well over four hours, depending on traffic.

One of my favorite vacations is to settle down at a hotel in central London, and do day trips to other cities. I buy a Britrail flexipass, only available to non-UK residents, and go by train.

Depends. London has somewhere between 5 to 7 airports depending on how you are counting. See https://www.google.com/search?q=london+airports+map&safe=off&tbm=isch&imgil=GugOdy249I7MqM%253A%253Bz9X8_JvMEee4AM%253Bhttps%25253A%25252F%25252Fwww.privatefly.com%25252Fprivate-jet-hire%25252Flondon-any-airport-A8220.html&source=iu&pf=m&fir=GugOdy249I7MqM%253A%252Cz9X8_JvMEee4AM%252C_&usg=__VRK_bMbBe7wzfmXwNukiYDwNKIE%3D&biw=1868&bih=871&ved=0ahUKEwjv0_mNisDVAhVB4yYKHYAlDikQyjcIMw&ei=7beFWa-pCcHGmwGAy7jIAg#imgrc=GugOdy249I7MqM:
or http://www.visitlondon.com/traveller-information/travel-to-london/airport/london-airport-map#zzCYGQLxlZ0DvJgG.97

If you want to find out non-stop destinations from each airport, you can use this nifty little tool: http://www.flightconnections.com/

None of them would qualify as "easy" or "convenient". London City is the closest but it has very limited destinations. I'd say 30-45 minutes from St Pancras.

The largest airport is Heathrow, it's one of the largest airports in the world and your travel time will be significantly depending on where in Heathrow you need to be. It has a very fast train connection to the city via Paddington. Unfortunately it's also very expensive but you can do it in as little as 30 min. Much cheaper and slower is riding the tube on the Piccadilly line. Runs directly to St Pancras/King's Cross. 1 hour minimum.

A good compromise is the "Heathrow Connect", which is basically the same train as the Heathrow Express but it has a few stops along the way. It takes maybe 10 minutes longer but it's only half the price.

Second largest airport is Gatwick. It's also quite large, so you need to budget ample time to get through security and to your gate. The only sane option is taking the Gatwick Express from Victoria. Maybe an hour or so.

I don't have enough experience with Luton, Stanstead, Southend to comment intelligently.

Most convenient payment system is the Oyster Card. It works for the Tube and the Gatwick Express, but not for Heathrow Express or Connect.

Don't even think about driving.

If you really want to get to the airports there is useful information on this link to another Q&A here but as others have said to get anywhere in England the train is liable to be a better bet unless you can get a really cheap flight. If you are going to Scotland you might consider flying but you could also consider the sleeper from Euston which is close to St Pancras. The advantage of this is that your travel takes place in the dark and you maximise your time in Scotland. Details with pictures here