PPRuNe is a great place to start. There is no easy way to become a pilot, and 99.9% of wannabes have to self-fund. It's expensive, but I like to think of it as an investment (it softens the blow)!
There is one full sponsorship offered by GAPAN per year for a wannabe to train for their fATPL, but the selection process is tough. They also prefer people who have taken steps towards earning a PPL, as this shows they have a firm interest in aviation. I imagine that they would prefer to sponsor UK citizens rather than us across the water because after all they are a British organisation.
There are also cadet sponsorships offered by Atlantic Airlines and Highland Airways, from Coventry ENG and Scotland respectively. These sponsorships require all applicants to have a PPL, often with more than just the minimum hours. Both of these operators use old turboprops in their fleets, and they are normally used for cargo. If you are accepted by either Atlantic or Highland, you will be bonded to them for at least four years. I wouldn't expect to be doing as much flying with them in comparison to other airlines either. Still, they do pay for you training after PPL!
The aviation industry is after redefining the meaning of "sponsorship". From time to time, airlines will offer a "sponsorship" scheme whereby the student will pay for all his or her training, but after graduation, if the airline still has the same recruitment policy, the graduates will be hired. A good example of this at present is Cityjet and Sigmar's IAA integrated course, so I won't go into further detail.
Obviously, self-funding has to be considered. This is where the Bank of Mum and Dad is needed! Modular courses can be done for a (much) lower cost than integrated courses, but whatever route you choose, expect to part with at least ?50k (Have a look at the "never-ending Modular v. Integrated debate" on PPRuNe). If you decide to look at integrated courses, beware of all their marketing bu*lsh*t. OAT (Oxford) are probably the biggest offenders. Glossy brochures with pictures of 737s does not equal a good FTO. Before deciding on any FTO, don't just talk to the propaganda pushers in their marketing department, but also the instructors, and talk to students both past and present, without the instructors around! OAT give employment figures for graduates which are not entirely accurate, as they include people in hold pools (i.e. waiting for a type rating), and considering their huge class sizes, are not impressive. I don't mean to criticise only OAT, but people have to be made aware of their short-comings (they really do have nice brochures!). Wherever you train, politics can/will enter the equation, because if you don't share the views of the management of your FTO, you won't get a recommendation, even if you are the best pilot since..........you get the idea?
For me, OAT is out of the question, because of the negative views of the students. It is also the most expensive, with the course costing ?90k+, and accomodation costing ?150 PER WEEK! And that is meant to be ?sterling not ?euro! Not to mention food! Also, they supposedly have recently fired a very good ground school instructor.
Aer Lingus are currently calling back the 2001 cadets, at least the ones who are still in aviation. If they ever start another cadet scheme, I doubt it'll be the same.
Basically, before you decide on where to train, talk to the instructors, and talk to the students. Choose a FTO that suits you. Don't think for a second that the FTO owe you a job, no matter how much money you spend. Sorry for the OAT rant, but in all fairness, even Eddie Hobbs would have trouble comprehending what a complete rip-off it is to train with OAT!