The recent UK infection numbers look very encouraging; under 9,800 cases today, yesterday was just under 11,000 IIRC. Hospitalisations declining steadily, and the deaths are pretty low now as well. Its dropping pretty quickly, which suggests either the virus is really slowing down a lot, or that the people who are now getting infected aren't being made ill enough to even bother with getting a virus test to confirm what they've got.
The strategy of giving as many first doses as possible before worrying about the second doses makes a lot of sense. You don't need to gold plate the vaccination programme, you just need enough people to have sufficient immunity to prevent the hospitals being overwhelmed with virus cases. On the face of it, even with only a quarter of the population having a degree of immunity, plus those immune through having already actually had the virus itself, we are now seeing a significant reduction in transmission. The true number of infections will be way more than the official 4 million, especially in the early days with virtually no testing being done, so it's quite possible we now have as many immune through previous infection as we have through vaccination, so getting on for half the population already.