I have a rare but serious heart condition that also tends to freak out insurance companies. However, I've found that if I get a letter from my cardiologist and my GP saying that there's no reason to expect anything to go wrong for period x-x, they're happy to either insure me, or to insure if I pay a premium.
When I was in NZ, Mike Henry Travel Insurance would do this, as well as Southern Cross travel insurance. They may have international branches?
For my current trip, I'm actually with World Nomads, although I don't think they're UK based.
Good luck - there's always a way, often your doctor might be able to suggest a company as well, or write extra documentation about it. He may offer to say that if you agree to carry medicine x or y with you they'll reduce the premium, or something - there's usually some way to do it, even if it's a high premium.