To those others experiencing this issue, I may have found something that will help.
I installed and a different SMS client (Chomp) on my phone, and SMSs now seem to be received MUCH more predictably. Don't know if this is coincidence or not, but it might be worth a try for those still having trouble.
P.S. My first vaccine appointment was delayed by this fault by the way. I hope no one actually died because of Virgin's inaction on this. I've now had both shots but I had to actively pursue them rather than wait for the SMSs as the government were instructing everyone to do.
We do thank you for popping back with your update @RockMobster - we can only apologise about the issues with your SMS service. This is only impacted when WiFi calling is activated and as mentioned earlier in the thread, it is being investigated.
Glad that you have since been able to get fully vaccinated.
I'd guess given the length of time being taken that it's not being given much priority given that in the current climate it could actually have been life-threatening? Not allowed out; can't get SMS at home; vaccination service relies on SMS; govt advice is to wait for SMS and not contact NHS in case it is overwhelmed; lack of vaccination may lead to death. Sounds like it ought to have been important no?