From multiple people I know who work in hospitals, there are a shocking amount of people in their 50s and 60s admitted due to covid.
God knows when the majority of those age groups will be vaccinated. They're all of the opinion that there's little chance hospital cases will be low enough to end restrictions by February or possibly even March.
There's about 15 million over 60's, if we assume that those over 60 make up 2/3rds of those being hospitalised (with most of the rest being over 50, as that would tally with what's been highlighted in the quoted post and is a very much worse case compared to the post after it which suggested 2/3rds of hospitalisations were over 80's) then to get everyone on that group to be vaccinated by the end of February would be about 1.75 million vaccines delivered a week (although this figure would likely need to be higher due to the need to start to deliver second doses and to show for the ramping up from the current rate of vaccination).
However it may well be that we get to the same point with less than that if the 2/3rds being admitted to hospital weren't the over 60's but were the over 65's, over 70's or over 75's.
However, end of February was suggested as when we should start to see cases to be coming down quite a lot, but that is then balanced out by the need for a few weeks for the vaccine to be giving the best protection.
However even at a 50% rate of protection for the 2/3rds most at risk we'd see cases fall by 1/3rd of what they otherwise would be. However hospitalisation rates could actually fall further than that if having been in the unlucky 50% to contact the virus the vaccine then provides a further 50% reduction in hospital admissions.
If that's the case then hospital admissions could be at half the rate that they otherwise would be (even allowing for the 1/3rd of hospitalisations being unvaccinated).
However the level of protection could well be higher than that which would reduce the rates further.
However even at 25,000 a day we'd have reached the point where we'll have seen at least 10% having had a positive test result for Covid-19 by the end of February. Add that to the 22% over 60's and it's likely that during March that we'd get to about 1/3rd of people having been vaccinated or having got protection having had it already (I know that there'll be lots getting the vaccine who will have already tested positive and that the level of protection isn't 100%, but then there's quite a lot who are asymptomatic who would easily balance that out).
However it's likely that those in urban areas (those at the highest risk of infection and therefore the highest R values) would actually be those who would be the most likely to be around more people with protection (bearing in mind some areas have seen above 1% of the population infected in the last week, so getting to 10% having had it may have already happened). As such that's going to further reduce the rate of spread.
Whilst that's not enough to stop it spreading (that's typically at the 2/3rds mark) it would certainly slow it down. In that if the R value with no restrictions is 3 then typically for every 3 people it tried to infect 1 would have protection and so the growth curve would look much flatter.
R value of 3 then after 10 weeks 1 case becomes 59,000.
R value of 2 then after 10 weeks 1 case becomes 1,024.
Now whilst that's not enough to get the number of cases falling that's with no other restrictions.
With other restrictions an R value of 1.4 becomes 0.93 and so cases would start to fall. With the potential for the rate of hospitalisations to be falling quite a bit faster in percentage terms than the number of cases.
As such, whilst March would likely still be rather optimistic (however it's certainly not beyond the realms of possibility) for removing of all restrictions it's certainly likely that we could see many areas moving down the tiers.
Right now many would be reasonably happy to be in tier 2 (rule of six but with no mixing of households inside) and there being the ability to see that they could reach tier 1 (rule of six) in a few weeks with more vaccinations.
March would likely start to bring better weather and therefore slightly lower case numbers anyway as well.