Well, the vaccine doesnt make you immune to Covid, and it doesnt stop you from catching it. It just massively reduces the severity of your symptons
So in itself, the number of cases increasing doesnt scare me that much - although the level at which they are at isn't great.
The problem is the risk of mutation, and the efficacy of the vaccine.
We know <70% of the UK population is double vaccinated right now. 60% of people in hospital are unvaccinated, 40% are double vaccinated. The efficacy of the vaccines are typically reported around the ~90% level, so let's just use that for now. I dont have a true population/vaccine weighted figure, not sure if one is available.
So, let's start some maths:
If the efficacy of the vaccine is E, and we assume the probability of going to hospital without the vaccine is the same as with the vaccine (2x dose) but not impacted by the vaccine (e.g. it doesnt take) is (1-E) * P_H, then based on 30% unvaccinated, 70% vaccinated, you'd expect:
0.7*(1-E)*P_H + 0.3*P_H = population of people in the hospital
What we know from reality is that 0.3*P_H is roughly 1.5* 0.7*E*P_H (60% of people are unvaccinated in hospitals, 60/40=1.5)
Therefore:
(0.3*P_H)/(0.7*(1-E)*P_H) = 1.5
P_H obviously cancels out nicely (by design) here
0.3/(0.7*(1-E)) = 1.5
(1-E) = 0.3/(0.7*1.5)
Efficacy therefore is about 71.5%. That's way below the 'advertised' rates, and I think that number only gets *worse* if you account for the people who should have had some impact from the first dose.
Obviously this is really naive and simplistic - but its a useful starting point.
The other concern, then, is that if you let it spread without check, it will continue to mutate, and there's a risk it will mutate into something deadlier, or not impacted by the vaccine. I think we already see signs that (as demonstrated above) the vaccines arent as efficient as people think they are for the Delta variant.
The hospitalisation rate is the key thing - its all about whether the hospitals get overwhelmed or not. But the virus is spreading like wildfire, and we're lifting all restrictions. That's the concerning thing for me right now.
We'll see over the next 2-3 weeks where things end up, but bear in mind (for example) you wont have to isolate anymore in the UK if you're double vaccinated I think in 3 weeks time? If theres only a 70% impact of that, then suddenly holy shit its going to spread rapidly among the vaccinated.
The big question will be where the UK's new cases are in 2-3 weeks time, imho.