The UK government is doing a fine job with vaccinations, which started in December 2020 and really got up to speed in January 2021, averaging 2.5 million vaccinations per week. These appear to be driving down new infections (all data from Worldometers.info):
That is, until you look at daily new cases in other north European countries which have barely started with vaccinations. In these three countries, daily cases also peaked in late December or early January and have been falling since then. I am aware that you could also cherry pick countries which show a slightly different pattern, but that is not the point. More things for which there is no obvious explanation: