NATS don't have stricter requirements
.
The CAA set the requirements for the initial Class One one and its the same for anyone wanting to be an ATCO anywhere.
Prior to the medical appointment tell your optician that you need to meet unaided CAA Class One Medical Requirements, if they stare blankley at you, go somewhere else.
At the moment, the CAA have slightly different requirements for ATCOs and Pilots with regard to the Class One but that will change and then the stricter JAA pilot requirement will also apply to ATCOs.