class 1 initial issues
The link you found certainly allows you to find your geographically nearest AME, but sorry to tell you this only applies to renewals of existing Class 1 medicals.
ALL initial issues of JAR class 1 certificates in the UK have to be done at Aviation House at Gatwick. There are a few tiny exceptions, such as those converting from Class 1 certificates in other countries, and some recent ex-members of HM services, but these probably don't apply to you.
Start saving for the train fare to Gatwick . . . . . . . . . !
And good luck with the medical !