Besides the RAF is there a way of becoming a pilot without spending tens of thousands of pounds on flight training? I'm finishing university and looking to go into a career in flying, I can't join the RAF since I am partially colourblind so I would not be allowed to train as a pilot in the Air Force.
There's a finite minimum set of requirements you must meet to get that ATPL and type ratings, and there's a finite minimum cost associated with that.
Nothing's going to change that. The only thing you can possibly, maybe, change is who is going to pay that money.
So don't fail any of the tests. The ONLY way to reduce the cost is to complete the training in as short a time as possible. Which means minimising flight hours, simulator hours, and retaking of courses. All of which boils down to passing every test first try.
And it will still take tens of thousands of pounds.
Going the Air Force route is also takes tens of thousands of pounds, except the air force (and thus other people, taxpayers) pick up part of the bill.
Same with every other scenario in which you're not paying everything yourself. Someone, somewhere, is paying for it.
Used to be (and maybe still is, but it's unlikely given the glut of unemployed pilots) some airlines would take on people and train them from scratch. But that's now rare. Most at the very least require you to have your PPL already, and many won't hire you unless you are qualified on at least some aircraft in their fleet.
Another possible option would be to move to another (probably non-Western) country for a while. Southeast Asia in particular is experiencing a large amount of growth in airline traffic and seems to hire lots of American, Australian, and European pilots, so you might be more likely to find openings in a program there that would cover the cost. The Middle East might also be an option, given their current huge growth in airline traffic, though I'm not sure what their hiring policies are like.
Cathay Pacific is an example of such a program in Southeast Asia. Among their listed programs for hiring flight crew is their Cadet Pilot Programme. They hire people from all over and send them to a flight training school in Australia. I remember them even advertising this program on the plane the last time I flew with them (a couple of years ago.) Being a former British colony, someone from the U.K. would probably fit in well there. I think every pilot I had on my last trip with them was either American, British, or Australian. Seems like it would be a fun airline to fly for, too, if you were ok with moving to Hong Kong for at least whatever their commitment period is. With the vast majority of their flights being international on wide-bodies, you'd likely get to heavy jets much more quickly than you would in Europe or, especially, the U.S.
One additional thing to note, though, as I mentioned in my comment earlier, if you don't meet RAF's requirements due to your eyesight, you may also have trouble getting the necessary medical certificate for an Airline Transport Pilot license, especially in Europe or the U.S. It turns out the EASA's requirement's regarding color vision are pretty much identical to the ones I mentioned in my comment earlier regarding FAA standards. According to the UK CAA:
(a) Applicants shall be required to demonstrate the ability to perceive readily the colours that are necessary for the safe performance of duties.
(1) Applicants shall pass the Ishihara test for the initial issue of a medical certificate.
(2) Applicants who fail to pass in the Ishihara test shall undergo further colour perception testing to establish whether they are colour safe.
(c) In the case of class 1 medical certificates, applicants shall have normal perception of colours or be colour safe. Applicants who fail further colour perception testing shall be assessed as unfit. Applicants for a class 1 medical certificate shall be referred to the licensing authority.