Apparently there is an app which your instructor can provide.
When my daughter failed her test about 5 years ago, the waiting list was about 14 months for a retest. Her instructor gave her a link which allowed her to book a test (which actually started in Edinburgh) and then got changed day by day to a date about 4 weeks ahead at our local test centre.
It automatically notifies you of dates and centres available and you can swap and change without any further cost and is only available to those who have taken and failed their test.
I can't remember the name of the link and I believe (IIRC) it was encrypted, but might be worth speaking to your instructor.
Yes, it’s definitely possible to move your date forward without losing your current booking. Some apps track cancellations at multiple centres and notify you as soon as an earlier slot opens up — they work even if you haven’t failed a test before. It’s usually just a matter of logging in regularly or using one of those tools to do the checking for you.
Instructors sometimes have access to useful resources too, so it’s worth having a quick word with yours.