A surge in infections has plunged countries across the continent into a fresh crisis.
Scientists are concerned Europe could be a breeding ground for stubborn new variants – and even trigger a fresh spike in cases here.
Currently only travellers returning to Britain from 35 red-list countries must quarantine in an airport hotel.
Other travellers are meant to self-isolate at home and take two tests.
And even though overseas holidays are off limits until at least mid-May, 461,000 people passed through Heathrow last month, including 118,000 EU citizens.
Prof Christina Pagel, right, of the Independent SAGE group of experts, wants stronger travel restrictions.
She said: “You can’t have this idea that some countries are safe and some aren’t – that’s just not true. We need stronger border control. If we want to rely on vaccinations being our way out of this, we can’t afford to import new variants.”
Prof Pagel, of University College London, added: “We have largely bet the house on AstraZeneca, which works brilliantly against the Kent variant, which we have now.
“But if we have a lot of the South African variant then it could be an issue for us.
“The other issue is if Europe has a big third wave, that provides more opportunities for new variants to emerge. We could get away with it, potentially, if we are lucky. I just wish we didn’t rely quite so much on luck.”
Her colleague Dr Gabriel Scally favours more quarantine. He said: “This third wave in Europe is really serious and has implications for the UK. The more the virus grows and spreads in Europe, the more the chance of even more variants cropping up.
“It is very worrying and has really serious implications on us removing restrictions. We should consider expanding the countries on which we have travel restrictions.
“My personal view is that we should move to quarantine instead of self-isolation.
“The virus is upping its game and we have to be very careful about how we go forward.”
Professor Paul Hunter, an infectious disease control expert at the University of East Anglia, warned: “We are not out of this yet and we still have to be cautious. If any country is still struggling with the epidemic, why would you want to go?”
The third wave in Europe is being driven by the dominant Kent variant. But scientists believe up to 10% of cases involve the South African mutation. The variant is not dominant in the UK or rising fast – but it is increasing here, say experts.
One new strain in France appears to go undetected in standard tests. Cases have soared by a quarter in France, and Paris has gone into a month-long lockdown.
Most of Italy is under restrictions after a near-doubling of cases and Poland has curbs for three weeks. Germany is set to lockdown after an “exponential” rise in cases and parts of Spain have toughened restrictions too.
Jens Spahn, the German health minister, warned: “We are in the third wave, numbers are rising, the proportion of mutations is large. There is not yet enough vaccine in Europe to stop the third wave through vaccination alone.”