How much aviation experience do you have to be sure that you enjoy flying enough to be a career pilot? You are at a good age to start training but first get some flight time in to be sure you want to continue.
When I was in West London I used to train at High Wycombe on weekends but I had my own car and was able to drive there. I ended up completing my training in Florida due to cost and weather. Training once a fortnight (or less) due to weather is not a cost effective way to progress your training so I saved up and got it done full time, one rating at a time, in Florida.
As was pointed out above it is much cheaper training and flying in the USA but if you want to fly in Europe they will want European certificates. Plenty of advice is available elsewhere on how to go about getting those after you have your FAA certificates. The systems are quite different, in particular have a look to compare the requirements for the ATP written in the two jurisdictions.
Study hard and if you are really enthusiastic you will find the time and money to do some flying. There are plenty of fields around southern England you could get to on weekends and holidays where you potentially could find paid work, meet people, explore work and career options.
Your presentation, enthusiasm and general attitude will determine how you are received and whether or not you are offered work or flying time. Just be careful you are not exploited. After spending time around the hangars you should have some idea if you want to train in the US or Europe and of how you could afford it.