I'm afraid I don't know the answer either but UK controllers don't get JAA medical certificates - I think they still use what was pretty much the same standards as the old CAA pilot Class 1 which may wel have more stringent eyesight criteria.
Sometime soon the harmonised European ATC licence will be introduced and there will be common medical standards although,
AFAIK, they will not be the same as JAA certificates. And I think they'll still be Class 1, 2 and 3 but Class 3 will be the most stringent.
The bottom line is that if you've got a Class 1 certificate for flying I can't imagine that you wouldn't be eligible for a controller's certificate but the only people who'll be able to tell you for sure are the CAA Medical Department. I wouldn't bother with an AME and you might be best asking the CAA to drop you an e-mail confirming the paperwork that they'll accept. Call me a cynic if you will but the last bit of advice is based on experience!