regardless of severity, my GP surgery does not offer appointments if you call them. It's the on line form that's several pages long. It can be difficult for some to explain what's wrong. It's then triaged, and if they decide what you've said needs an appointment then they call or email.
the OP didn't explain what type of extension. Mine was extending exempt entry by 30 days. Other extensions like based on retirement/marriage etc would be different perhaps.
what sort of extension are you asking about? A 30 day exempt entry extending for 30 days? Or are you asking about a 2 year extension based on "something else"