You need to stop focussing on cases. Cases are absolutely irrelevant.
As posted above - there is a clear link from cases to hospitalisations. They are a leading indicator of what is most relevant.
Cases are currently rising exponentially, with a doubling time below two weeks. Hospitalisations are rising at what seems to be a fairly consistent 5% of cases, only half what it was before the vaccination programme.
The lesson of the pandemic is that focussing on *today's* issue - "incredibly low" deaths and inpatients as you state it - will be very rapidly be overtaken by events unless we look ahead, and recovering from a wave is far harder than preventing it.
So, what do we expect looking ahead? Reasons that exponential growth will stop:
(1) Run out of susceptible people - everyone unvaccinated gets infected. Needs a huge number of infections.
(2) Summer and seasonal effects. Maybe, nobody can quantify, but should help somewhat.
(3) Vaccinations stop it. Absolutely should do, but very hard to know how soon. Wales gives us hope.
(4) People change their behaviour when faced with renewed proliferation. That's probably already helping in Bolton.
Reasons the growth will accelerate:
(1) Removal of all restrictions 21st.
So as things stand, today, we should expect hospitalisations to double faster than every two weeks for some time to come if we go ahead with a significant relaxation 21st June. I think they're somewhere north of 100 daily right now. If that doubles every ten days, we're over 1000 daily in a month. If it goes down to 7 days, 2000 daily in a month.
In that context, further relaxation is very hard to support,
with the data we have today. In a week's time, perhaps it will look different, though that seems increasingly unlikely. It also now seems very unlikely we'll have any kind of definitive view for the 14th when a decision will be made.
Of course, much is uncertain, as the modelling posted above by others shows. It may be that seasonal effects are large, we're already close to herd immunity, and the whole thing fades in a matter of a short number of weeks. Equally, a peak of hospitalisations comparable to January is still possible. The cost of delaying relaxation by a couple of weeks for this to become clearer is very low compared to the consequence of finding out we've set a route to a significant further wave by going ahead.
Here's that graph of hospitalisations as a % of cases (10 day lag) again:
