Alexi,
when you convert from FAA (or any ICAO certificate) to JAA you start with the 14 exams first. This can be done either as a distance learning course or as a residential course. Either way plan to spend from 8 months to a year on it. Classroom may save you a few months of study time and is a great option if you're not the most disciplined - it is allot of material to study!
You can find a list of ground school courses in the UK here -
http://www.bestaviation.net/uk/
The 14 exams are multiple-choice and require a 75% pass mark. Exams are conducted once a month and it is normal to split the exam sittings in two or three (sitting 5-7 exams each time). Each sitting takes 3-5 days.
Once you have passed all the 14 exams (try not to fail any - organizing a re-sit can take a couple of months...) it's time to do the JAA CPL conversion.
The CPL conversion is "training as required". Most places will quote you 5 hours and unless you're really current you will probably fly the five hours. The CPL skill test is done in a complex aircraft and there are a few differences in what they look for in the skill test that you need to be aware off.
Once you have your CPL you do your ME/IR conversion. Technically this is training as required with a minimum of 15 hours but many spend more than this. The major reason is the difference in operational procedures in Europe. You do more NDB stuff, ATC is a bit tougher to deal with (they're not as friendly as in the states) and transition altitude is 3000 feet as opposed to 18000' in the states. The IR skill test is done in a multi engine aircraft.
After your ME/IR you do an MCC course. This is not a pass/fail course. An MCC course normally takes two weeks and is done in a simulator. The purpose is to teach you how to operate in a multi crew environment.
Once all this is completed - about a year to 16 months from when you started......it's time to start applying for an airline and saving up the rest of your money (if you still have any).
Hope this was of any help. Good Luck!