No, there won’t.
There are so many legal, moral, ethical problems with this proposal I don’t even know how it could even be contemplated.
However it could be possible to have a vaccine or a 14 day (at the individuals expense) quarantine (probably at a designated location rather than in a home) as a condition of entry to the UK without hitting quite so many of those problems.
If you don't wish to have the vaccine then it makes it harder to travel, but not impossible. There's a lot less reasons why that would become a moral issue.
The majority of the population would see it as stopping new cases coming into the UK and so would support it, those who didn't always have the option of not going abroad, especially given that many other countries would likely have a similar rule.
For anyone traveling to a high risk areas they would certainly wish to have the vaccine anyway (in the same way as other holiday vaccines).
Such a rule would likely help to increase the uptake.
However I would guess that to get to >80% uptake would be fairly easy to achieve, as there's likely to be a fairly big proportion of people who would like things to return fully to normal. As well as many businesses applying pressure to their staff to get a vaccine (although still they'd have to be careful to not to discriminate, but a company wide communication with wording like "until we can return to the way things were before we can not be sure that all jobs will be secure" would probably be enough to focus enough minds to also help uptake).