The info on the DVLA website is not entirely clear.
https://www.gov.uk/driving-eyesight-rules
"You must tell DVLA if you’ve got any problem with your eyesight that affects both of your eyes, or the remaining eye if you only have one eye.
This doesn’t include being short or long sighted or colour blind. You also don’t need to say if you’ve had surgery to correct short sightedness and can meet the eyesight standards.
Check if you need to tell DVLA about your eyesight problem by searching the
A to Z of medical conditions that could affect your driving."
Any problem could be e.g.hay fever (itching eyes) or other common short lived condition. No one would tell the DVLA about those.
Migraines can cause severe visual disturbances to both eyes, but is not listed among the notifiable conditions. (BTW blindness is not listed either - that's gov. dept's for you. Cannot see the wood for the trees)
If I had double vision I would not drive, but I would wait for a diagnosis then check to see if it is in the list of conditions published by the DVLA.
At your eye test your optometrist will ask if you experience double vision. That is a standard question they all ask.