We have had different things in different areas (with 3 different coeliacs):
Mid Essex - no automatic call for checkup. If you want an annual blood test then when it's due request one. If you don't request it they don't seem to notice.
Cambridge - Not been diagnosed long enough to test the GP checkup system. When first diagnosed the coeliac clinic at Addenbrookes seems to be quite thorough with lots of blood tests and appointments to talk to the dietitian and a follow up endoscopy after 12 months.
Norwich - a call for blood test for vitamin deficiencies and vaccinations and a request to make an appointment for a chat with the GP.