Watching Boris Johnson continuously glancing down to read his notes to make an apology tells me that there's little, if any, sincerity in it.
He is simply reading a script and acting a part, and I think his biggest anxiety is how this is going to affect him, personally.
I've been watching and listening to him for some time and have come to the conclusion that in spite of his upper-second class degree in Ancient Lit. and Classical Philosophy (or whatever) - he is actually not very bright. He cannot debate coherently when left without a script to refer to and verbally wanders all over the place. It is, apparently, well known that he doesn't "do" detail, which I assume means he can't get to grips with briefs, documents, etc. He's from a privileged background and has probably never had to really fend for himself, like most working people who then learn how to cope with life and its humdrum daily grind, consequently he lacks the skills to deal with the basics. And I think it's made him lazy and incompetent.
As for the vaccine rollout which he trumpets at every given opportunity and uses as a shield against criticism. He didn't develop the vaccine himself, he didn't drive around distributing the vaccine, nor did he stand for hours sticking it hundreds of people's arms. He took a decision - after consultation with others - and said "let's go for it" (or whatever)... and good for him that he did, but others did the work and he's now covering himself in the glory of the hard work of others. He just cannot rest on this laurel wreath indefinitely.