He doesn't need to keep calling though. Those of us who have links but didn't get appointments at the time just kept checking and eventually there were some available. I'd still much rather have had the chance to book by being sent the link, than nothing! I don't see why he'd rather have waited til mid-April to get sent a link, and miss out on any potential spots, just so that it was a time when it was easy to book.
I didn't phone anyone. The link just eventually came up with some possible times, and I took one for the future.
If he's vulnerable, you'd think he'd want to get one as soon as they come available, rather than wait for weeks from now to be sent a link. The target is mid April for all the second wave of groups 5-9, and something like end of March for group 6 specifically, so there is a long time to wait yet before worrying.
It's been discussed loads in the news, how the group 5/6 split is working, so I don't think very many people are phoning or wasting time - they have been told on most of the GPs website that they'll be contacted with a link at some point in the future. When my link came, there weren't appointments available at the time, nothing showed up for a couple of weeks. You just keep checking.
I think they did focus on the most vulnerable and got them done by Mid Feb, for the majority. Now it's the somewhat less vulnerable, and they're hoping for mid-April. They can't go equally fast in all areas, so I don't think some should wait to do group 6 if they have capacity, even if other areas don't yet.