Cologne to Brussels then Eurostar to London - should take about 4 hours all told. For lots of great info on trains I always spotlight these IMO fantastic sites - www.seat61.com; www.budgeteuropetravel.com and www.ricksteves.com.

Go to www.eurostar.com to book online deep discounted tickets - paying far less than if you just show up. Go to www.bahn.de - German Railways site for similar discounts Cologne to Brussels or www.thalys.com. Early bird does indeed get the worm!

Cologne isn't exactly a low-fare haven when it comes to flights. You could take the ICE train to Amsterdam, and one of the numerous cheapie flights on EasyJet et all from A'dam to London. Or take the Thalys to Paris, and the Eurostar on to London.

If you want it really inexpensive, and have excellent Sitzfleisch and a high boredom threshold (about 10 hours), you could try a Eurolines bus:
http://www.eurolines.co.uk/

easy jet and german wings are two low cost carriers flying from Cologne or Dusseldorf to London.

Search on www.kayak.com or www.skyscanners for prices

or even www.skyscanner.net

It's sometimes possible to get cheaper fares on the train than on Easyjet or German Wings between Cologne and London - but generally the plane costs less. At 5.5/6 hrs, it's always a bit slower to travel by train (via Brussels, BTW: never via Paris) between the two centres - though you can obviously do a lot more with those 5 hours. Since you're unlikely to be going from a hotel next to the Hauptbahnhof to one next door to St Pancras (though that's possible and perfectly fine), those numbers will be different in your case.

Unless you're a train (or plane) fundamentalist, there's no huge difference, and no consistently predictable difference, between plane and train.

You need to cost both time and money between the two for the whole end-to end journey (transport to and from airports always takes longer than the flight time and often costs more than the flight) for the day and time that suits you (a trade fair in Cologne, for example, can change the balance completely. Which way depends on the industry).

Beware of ideologues insisting one way's "better". They're either selling something they get a commission on, or arrogantly assume your priorities are theirs.

For simple train timetables, start with www.bahn.de. You'll have to book through Rail Europe or Eurostar.

Unless you're a train (or plane) fundamentalist, there's no huge difference, and no consistently predictable difference, between plane and train.>

In which case take the train and actually see something of the European in between Cologne and London and not just see airport tarmac and London - experiencing the Chunnel train IME is great and riding the up to nearly 200 mph trains are another experience. And spouting volcanoes are unlikely to suddenly scrub train travel. But if one is significantly cheaper than the other well then cost is a factor of course. But if as flanneruk says there is not difference then see something along the way as you do on the train - and trains are infinitely more comfy than planes and their cramped seats - and airports can be hectic - getting transportation into London from Heathrow can be expensive if not taking the snail slow tube.

For simple train timetables, start with www.bahn.de. You'll have to book through Rail Europe or Eurostar.>

Well for cologne to Brussels tickets you can book directly on www.bahn.de - no need to go to RailEurope - easy to book discounted or full fare tickets directly on www.bahn.de - that is if it is a German ICE train that runs that route. For Thalys train www.thalys.com.

my understanding is that you can book all the way through with eurostar - and in that case they will honour your ticket in the event of delays and get you on the next available train.