The party said the current so-called travel roulette, where countries are being slapped with a 14-day quarantine rule for travellers returning to Britain with only days notice, is having a “dire” impact on the travel industry.
Shadow home secretary Nick Thomas-Symonds said a “robust testing regime in airports” could minimise the need for those returning from countries with high Covid-19 case rates to self-solate.
In a letter to Home Secretary Priti Patel, he added that he had “serious concerns” about the low-level of monitoring of incoming travellers, claiming “less than a third” of passenger quarantine forms are checked.
Ministers have been making weekly decisions on whether to reimpose travel restrictions where the risk of infection is escalating, using 20 cases per 100,000 people as a threshold to add or remove countries from the “red list”.
In the latest rule change, which came into force on Saturday morning, the Scottish and Welsh governments re-added Portugal to their quarantine lists but England and Northern Ireland did not.
Holidaymakers in France, Spain and the Netherlands have been left scrambling to get home in recent weeks as ministers have introduced quarantine curbs, sometimes with only hours notice.
In his letter to Ms Patel, Mr Thomas-Symonds said: “I write to call for a rapid review to fix chaotic quarantine arrangements that are losing public confidence and undermining our ability to keep people safe and save jobs.
“In order to rebuild this trust I am calling on [the] Government to undertake a review into quarantine policy, to report within a fortnight.
“It should include outlining options for a robust testing regime in airports, and related follow up tests, that could help to safely minimise the need for 14 day quarantine.
“It is clear that ramped up testing is an important part of trying to respond to the pandemic and safely reopen society.”
It comes as the Metropolitan Police said it had received 1,000 tips since the start of August from UK Border Force officials to check travellers were self-isolating, and visited 840 individuals, the Guardian reports.
Greater Manchester Police received 263 such referrals.
In more confusion among holidaymakers, Scotland has imposed self-isolation rules for Greece and Wales has done the same for six Greek islands, including Zante and Crete. However, Westminster and Stormont have so far resisted.
Airlines have criticised the use of quarantine measures as they face a jobs bloodbath.
Virgin Atlantic announced on Friday its plans to axe another 1,150 jobs after completing a £1.2 billion rescue deal, following 3,150 cuts in May.
A Government spokeswoman said: “We are taking clear and decisive action to slow the spread of the virus and save lives.
“We keep the data for all countries and territories under constant review, and if the public health risk of people returning from a particular country without self-isolating becomes too high we will not hesitate to remove countries from the travel corridors exemptions list.
“Work is ongoing with clinicians, the devolved administrations and the travel industry to consider if and how testing could be used in the future to reduce the self-isolation period.
“Any potential change to the testing for arrivals would need to be robust in minimising the chance that positive cases are missed.”