UK industry bodies have again pushed the government to allow "travel corridor" deals with other countries.
They want to know when and how ministers will agree deals with other countries so more people would be exempt from new quarantine rules for people arriving into the UK.
The business and university groups say it is vital for the economy that the UK begins to open up to trading partners.
The government said it was continuing to consider such travel corridors.
A range of organisations representing businesses across the UK have written to ministers asking them for clarity on how and when the government might relax travel restrictions.
The bosses of groups representing industry, tourism, hospitality and universities, as well as regional and national chambers of commerce said it was "vital" that the UK began to open up for trade.
Business campaign group London First, which organised the letter, said over 1.5 million jobs across the UK are supported by air transport.
In a letter to the home secretary, the foreign secretary, and the transport secretary, the group made three demands.
They want more detail on how and when the government will agree travel corridors with countries with low infection rates, so passengers on certain routes will not have to self-isolate for two weeks when they arrive in the UK.
They also want to know when the Foreign Office will move away from its current blanket advice against all but essential travel abroad.
They argue a more nuanced approach is needed, based on the risk posed by individual countries.
Finally they call for a more comprehensive strategy on health screening at the border. They say businesses have to plan, so they need to know when journeys abroad might be possible again.
"As we look to recover from the economic shock that Covid-19 has delivered, it will be vital that we start to open the UK up to our trading partners," the signatories said.
The groups, which include the Confederation of British Industry (CBI), the British Chambers of Commerce (BCC) and the Federation of Small Businesses (FSB), said that whole sectors of the UK economy "simply won't recover and thrive without international connections".
Business and tourism groups have been urging the government to relax quarantine restrictions to aid the UK economy.
A government spokesperson said: "We recognise this is a challenging period for businesses and have announced an unprecedented package of support measures to help them, while also trying to avoid a second peak of this deadly virus by managing the risk of cases being imported from abroad.
"Our focus is implementing measures which help tackle the spread of the disease and protect public health. The government is continuing to consider the travel corridors concept as a possible way of relaxing border measures and increasing travel once it is safe to do so.
"We are monitoring the global travel situation closely and keeping our advice against all non-essential travel under continuous review."