How did YOU make it to be a pilot?
If you shop around you will find an integrated or modular course for less than your specified budget. You can find those courses in Easter Europe and more specifically in Greece. You will finish with an EASA licence, just like anyone else would at more expensive schools. If you really want your licence to be issued by CAA, after you get your licence you can apply to CAA to convert your licence.
More importantly do not pay for a type rating because that's one of the reason the industry is going down. Get a job in the general aviation for a year or two and you will improve your flying skills a lot and end up with more money than paying for a type rating and get into a shiny. And having a type rating without experience does not mean your chances of getting a job will increase much.