London - how to get there and where to stay
The first is getting there.
That part is pretty easy. And with increasing competition in the air, it has become rather cheap, too, compared with just a few years ago. So far I've been flying (at least) SAS, Maersk, Varig(!) and Go!. But be careful: when we flew Go! we bought the tickets well in advance only to find out that SAS - a little later - made an even cheaper offer (too cheap according to Go!) in the summer months. So if you're going from Denmark I urge you to check at least SAS, Ving, Go! and Gate Eleven which we've all used; but there are others. Recently (2004) we've used Flybillet.dk.
Being DKish I can of course only make suggestions for flights from DK, but I'm sure there must be similar - or maybe even better? - bargains from other countries. And if you're not familiar with the London Airports, in my opinion it doesn't really matter whether you fly to Heathrow (which is probably the most well-known), Gatwick or Stansted; in all cases there are excellent train services to central London which take only 30 - 45 minutes. To some extent Luton is now also considered a "London Airport" (and is actually a little closer to London when looking at a map (which I do a lot:-) but I haven't yet flown there myself.
Where to stay, then?
This clearly depends much on personal preferences - and how much you're intending to spend. We have successfully found good, affordable accommodation through travel agencies, e.g. Gate Eleven. Or you may venture out on the Net and find a hotel yourself; we've done that, too, and successfully used Hotel Connect. For the last trip (2004) we happened to use TravelNow.com and ended up at the Enterprise hotel near Earl's Court. (Mixed impressions on that one - which I may write down one time(?) But using TravelNow worked fine(!))
One thing you should look out for is where the hotel is located. There is quite a lot of traffic in central London, so I urge you to not just listen to the description of the hotels - funnily enough almost everyone is located in a quiet neighbourhood - but also check the address on a map which you can also do on the Net; see my section on maps.