Steve,
I doubt very much whether you will be able to get it exactly perfect by manual heating and bending, purely because when annealing by hand, it will never be exactly the same softness all along the rod and that will cause flatter areas than others. The only way to achieve consistent annealing would be to use a kiln where the whole length would be temperature controlled.
What you require is someone who has a rolling machine with ring grooves, then you wouldn't even have to soften the metal, it will curve it whilst still in a hard state.
The 12" rolls on my 3 in 1 has the largest ring roller at 6mm, so going by that, maybe a normal roll set of 12" would be OK. You would have to contact the supplier to see what the max diameter of material it will form into a ring. The overall diameter of the job shouldn't come into the equation, just the diameter of the bar.
I don't know where you live in the UK, but maybe another member within easy striking distance has a set of rolls you could use.
I think Ralph has a set in north Wales, mine are in south Cheshire and I am sure if there is anyone else nearby to yourself, they would be only too willing to help you out.
If you only wanted a couple or three parts making, it might be cheaper to take up the offer of help rather than fork out a fair amount of cash for the machine. But if you could use one again, only then consider buying one. They are a thing not used very often, but when they are needed, having one is indispensable.
http://www.rdgtools.co.uk/acatalog/FOLDER_S___BENDER_S.htmlBogs