Control jobs are very competitive. The two usual routes tend to be via other railway operational grades, or equivalent roles in other industries (police control, armed forces, etc.) What they are effectively looking for is proven experience in quick thinking, decision-making, communicating, working under pressure, leadership etc. as well as an understanding of how the railway works. That's not to say you're not in with a good chance - some Controls seem to be more open to external candidates than others and many controllers have been from outside the industry and still proved themselves.
Coming in fresh to the industry, you'd probably be looking to start as a Train Delay Attributor or Customer Information Controller, but putting in applications for more senior roles could potentially yield results.
As long as you have your GCSE Maths and English, qualifications aren't necessary.