The only published models have assumptions which have been proven to be false, so therefore any conclusions based on those models must also be false.
Sadly the people who "market" the models including PHE, do not publish them enough to re-run them with assumptions that are now closer to what is known. So we don't know, but models are not the things that suggest its true.
With current effectiveness of the vaccine, it is very difficult to get hospitalisations high enough to overwhelm (the individual chances of requiring hospitalisation is too low that way more people than previously would need to catch at it the same time, and even "no imposed measures" does not appear to facilitate that.
That doesn't mean restrictions wouldn't be warranted, but we are certainly near the point where it's not completely obvious that restrictions are better for health than no-restrictions unlike previously. So the people calling for restrictions need to make sure they tell us how many people their restrictions will harm, and what harm it will do.