It will all depend on the vaccine manufacturers fulfilling orders promptly
If we have to wait between deliveries then it could take much longer.
I doubt we will see much relaxation at all until at least priority 4 (CEV) have been done, and then most after priority 6 (CV)
It's 5 weeks from first jab to 'safety' (assuming you are not in the unlucky 10% for whom it doesn't work). Not clear when they expect to finish priorities 1&2 (the ones underway) or when further deliveries of vaccine will arrive