The two doses must be 28 days apart and only start working fully 2 weeks later.
At full capacity, if those numbers are right, every 28 days you can vaccinate 4,675,200 people. You then need to vaccinate the same people for the next 28 days.
If it takes till say the start of February for vaccination to reach full capacity, at that rate you can vaccinate 18,700,800 people by the start of autumn 2021. That's a lot, but it's clearly not loads.
More positively, there are 15.6 million over 60s in the UK, 1.2 million NHS employees, and 500,000 teachers, with spare capacity for another 1.3 million vulnerable people or key workers in that period. That makes it feasible to vaccinate all of them by September next year, that is by the start of that school year and winter flu season.
That to me seems a reasonable point to say that most if not all restrictions should be removed (but to be very clear: I'd imagine removing the harshest restrictions much sooner).
That timeframe obviously improves if some of the single injection vaccines can work, or if vaccination capacity can be increased. My calculations are probably quite cautious too eg you may well be able to get a couple of million in before February. Combine with summer conditions being worse for the virus and perhaps more bullishly the vaccine brings us close to normal by June?