At the start, hospitalisations tracked cases by about 2 weeks and ICU another week later. In the UK this is still the case through October, but cases were fairly flat (there were a couple of brief "waves" which peaked in cases about 2 weeks before hospitalisations). About 1 in 40 cases resulted in hospitalisation. Everyone who wanted a vaccine had had both well in advance of those figures.
In the last week daily cases have increased 50%. If this remains with the 1 in 40 case:hospitalisation ratio, then between Christmas and New Year we'll be looking at 2,000 new hospitalisations a day.
This time last year the ratio was 1 in 13 case->hospitalisations, so clearly things are far better.
However if cases are doubling every 4-5 days - with cases 4 days ago being abeing about 100k/day, in a few days time this will be 250k/day, and by christmas 700k a day. Before New Year it will naturally plataeu at 1.5m a day (because that's 1 in 6 of the population getting it in a week, and there just aren't enough uninfected people for it to go around.)
That seems to be the strategy the country is going for.
It's too late to stop it reaching 160k/day, which would be 4k hospitalisations a day - the peak of last year - based on October's admittance rates, and there's very little sign of attempts stop it going further, meaning we could be looking at 8k attempted hospitalisations come new year.
The main hope is that Omicron, combined with boosters (which already have a >80% uptake in over 60s) will reduce that 1:40 ratio