All new entrants to the UK, regardless of reason, should have had complete coronavirus vaccination before they travel to the UK otherwise travel to the UK should be denied. This would not effect quarantining, banned travel from red list countries or lateral flow testing.
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Our population will soon mostly be vaccinated against coronavirus, which combined with high summer temperatures should substantially reduce transmission virus in the UK.
This means that the greatest risk to this success is from importing a new strain of the virus in someone who has not been vaccinated. Vaccinated people are less likely to spread and transmit any form of coronavirus, so insisting on travellers to the UK being vaccinated should reduce the chances of further outbreaks of COVID-19 and will keep our economy open.