The culture secretary has told the BBC that coronavirus testing at airports is not a “silver bullet” to stop the need for quarantine.
Oliver Dowden said testing the measure was not enough because the virus can develop over time.
The boss of Heathrow said airports should be allowed to test for coronavirus to avoid the “cliff edge” of quarantine.
The travel industry is seeking ways to rescue the holiday season.
The government’s sudden change to travel advice for Spain at the weekend prompted a fresh wave of confusion and uncertainty to people’s holiday plans.
Heathrow chief executive John Holland-Kaye told the BBC the changes to guidance over Spain showed the need for an alternative.
He said he wanted the government to work with the company on the plan and he could have testing sites set and ready “within weeks”.
But Mr Dowden quashed the idea, saying: “We are not at the point where there is a viable alternative to the 14-day quarantine.”
Although he added that all options were under review.
Other countries are operating airport testing. It is voluntary – and free – at some German airports now although that may become mandatory, as it is in France for arrivals from high-risk countries such as the US and Brazil.
The Netherlands approach is to single out people coming from specific areas with high levels of infections – such as a few named regions in Spain and the UK city of Leicester and urge them to self-isolate.
Mr Holland-Kaye said a UK airport test would cost about £150 each, and passengers would be expected to pay.
He acknowledged that was “not cheap”, but that the test would come down over time as more people took it.
But he said there would be those prepared to stand the cost: “There are people who are worried about being able to go back to work or get the kids into school, there will be people who are prepared to pay that to avoid the extra period of quarantine.”
The idea of introducing testing at airports is an attractive idea. The theory being people could travel where they like and just get tested as they arrive back in the country, negating the need to self-isolate.
But the government is not convinced.
Why? Logistically testing all the travellers who arrive every week will be difficult.
Testing capacity has increased but this would stretch the system. Not to mention the practical difficulties of setting up testing facilities in busy airports.
But the other factor, which is perhaps more crucial, is that in the early stages of infection the test may not even pick it up.
Instead, officials are much more persuaded by a more intelligent, targeted approach to self-isolation.
That would involve asking only those coming from certain regions in a country where the infection rates are highest to self-isolate.
That could then be complemented by then asking them to get tested after a week, meaning if they test negative, there would be no need for the full 14-day self-isolation.
All this and more is being discussed behind the scenes.
Mr Holland-Kaye said: “The aim would be to have a test on arrival. We could have it up and running in the next two weeks, then we need to work with government to see what happens next.”
He said the plan would be for passengers to go into quarantine and have another test after eight days: “If they were infected we would be confident that it had shown itself. If it was clear, they would be allowed to go out of quarantine earlier than had been the case. It’s very scientifically based.”
Under current rules, those arriving in the UK from certain countries must self-isolate for 14 days.
The government has indicated that it is keeping all quarantine measures under review.
It is said to be considering an eight-day stretch between tests, whereas figures within the travel sector are keen for a five-day period.
The number of days required between each test is critical in reducing the possibility of “false negative” results.
A false negative result is possible if someone who has recently contracted Covid-19 is not showing symptoms.
Mr Holland-Kaye said the airport wanted to start up trials with Singapore and Canada.