I think the 'political optics' win for Johnson is going to more likely be: "We are the first major country to reach near full vaccination".
Bibi in Israel is facing intense political ambiguity, and they are paying 3-4x (for the vaccines) what other countries are paying, and have apparently been doing some behind the scenes shenanigans for acquisition, I mean it's Isreal, that's what they do (no offence to those who might take it that way but they are the most realpolitik country on planet earth). They are way ahead of anyone else and I suggest this is Bibi's political salvation plan.
Boris, similarly.
It's a little bit conspiratorial, but wouldn't be surprised if there are some behind the scenes actions by UK gov. to make sure the UK is first.
Also consider that the EU is frankly playing a losing hand and they look really bad from this.
This is a major existential crisis and if China, US and UK end up with full vaccinations months ahead of the EU it's going to be very, very damaging.
At minimum, the EU has to make a very big public stink about it to ensure people know/believe that the EU is doing what is possible, to mitigate the damage and possibly to be able to push the blame a little bit to others.
Finally - there's nothing wrong with the UK offering the EU help, and that it would also end up being good PR. The problem with the claim is not that it's 'sickening' but rather it's frankly not a huge material PR win. It's a nice thing but it's only worth a news cycle or two.
Having the UK immunized a few months ahead of the EU, irrespective of the underlying realities, is going to be something that will be remembered and analyzed for a decade.
Frankly, in the end, I actually think it's far too risky for any EU/UK politicos to be playing underhanded games, the blowout would be devastating. I just think it's a matter of operational reality that the UK is doing well on this (note they are doing very poorly on infections), though I do feel EU has dropped the ball on securing vaccines from a wider base. Even Canada has put in options to purchase from a variety of sources.