I do think zero restrictions is realistic by the summer, but I think the CRG timescale (all gone by the end of April) is rather optimistic. I could be wrong, but I'd expect all restrictions to be eased only once the majority have had their first dose and the vulnerable have had their second - so probably no sooner than late May or early June.
Having said that, as Nicholas Lewis says, I appreciate the way Steve Baker is making the case for a faster timescale, because it's a counterbalance to all the scientists demanding restrictions for many months to come. It means that a reasonable but ambitious timescale, such as "No restrictions by mid June", becomes the compromise option.