Johnson is right (could be the first time I've ever written that), and I've posted to that effect a number of times.
Most of the drop to date is due to the lockdown rather than the vaccine.
Compare the the USA: same vaccine takeup (near as dammit), 3x reduction in cases vs our 20x reduction (very approximate figures).
The vaccine didn't drive most of the reduction, but does allow us to open up.
Most modelling points to a potential significant surge if we just open up now. Not certain, but potential.
That said, the impact of lockdown and vaccines has been far better than I dared hope, so I wouldn't be against an acceleration, if things are still in the right direction in another three weeks or so.