So here's the update.
When I called Gatwick to ask if I could book a Class 1 medical, I was, as expected, asked for my glasses prescription.
To cut a long story short, they have invited me for a medical where the opthalmologist is going to examine my eyes more closely. The lady I spoke to said it was very positive, because if it was likely that my eyesight would fail the test they wouldn't have invited me. Fingers crossed....