Are the facts right? Yes and no. He doesn't need an initial class 1 , he needs a lapsed extended renewal Class 1, but yes, this has to be done in an Aeromedical Centre, and yes, at the time of posting they are all near London.
https://www.caa.co.uk/Commercial-ind...l-certificate/
As far as I know NATS at Swanwick are only offering initial EU class 3 medicals for ATCOs and not offering initial Class 1s for Pilots.
There is nothing to stop an AME "up North" setting up an Aeromedical Centre, but the investment in equipment and staff is large, and they would need to be sure of enough business to make it worthwhile.