There's loads of info on here if you use the search, but off the top of my head:
1. Get a Class 1 medical. No point doing anything until you have that. This involves going to the CAA at Gatwick and costs over £300 (plus your travel/hotel expenses). You could get a Class 2 locally, but just be aware that you still need that Class 1 before you can start CPL training, so it's desirable to get it first, then there's no doubt.
2. Do your PPL. Probably around £8k these days once you've bought all the required gear, decent headset etc..
3. Fly lots of hours. You need to get 150hrs total time, of which 100 is you in command. Cost? Varies - a lot go to the USA to do this. Anywhere between £5k in the states to £12k or more over here.
4. Do the ATPL exams. This requires an approvel groundschool course (between £1k and £2k depending on provider, plus expenses) which you must attend for specified amounts of time in addition to home study. Takes a year (give or take), there are 14 exams, each one costs over £60 to take. You must take them all within an 18 month period.
5. Once you've got all them, do your CPL course. You may or may not choose to combine this with a multi-engine rating. Anywhere between £5k and £10k.
If you didn't combine it with the CPL, do a multi rating.
6. Do your instrument rating. Mostly done in the sim, but it'll be at least £10k, probably nearer £15k with the flying portion done in a multi. CPL and IR must be done within 3yrs of passing your last ATPL exam.
7. Do an MCC course - hand-holding teamwork stuff for multi-pilot environments. A couple of grand, usually.
8. Now you need a type rating. The traditional route is that any airline who employed you would pay for this, and bond you to work for them for a specified number of years to essentially recoup the cost. In a market saturated with pilots wanting jobs, some have chosen to pay for this themselves in the hope it will make them stand out from the crowd. I believe a 737 rating is about £20k. Contentious issue as to whether you should or shouldn't.
You now have all the neccessary bits of paper to go and work for an airline as a first officer. Now... the reason you took the ATPL exams as opposed to the CPL/IR exams is that when you've logged 1500hrs, of which 500 must be multi-crew (ie. airline), plus a few other requirements, you are eligible to take the ATPL skills test. This allows you to legally command a public transport flight (ie. captain), although you'll need a load more experience before you start getting a sniff at promotion.
Basically it'll cost you a fortune, you'll spend many years living on the breadline and eventually, many years in the future you might, just might end up with a nice captains job and a decent salary.
If you really have money to burn, there's something called the integrated route. This is a full time course where you start from zero and end up with a CPL/IR. Some providers of integrated training have connections with airlines, meaning you might get a sniff of a job straight after your course. However you're essentially making a £20-30k bet on that, which is the difference in cost over doing it the modular way as described above.