Anyone arriving from overseas must currently self-isolate for 14 days unless they have travelled from an exempt destination but this list has grown thin.
Grant Shapps told the virtual ABTA travel industry conference on Tuesday that travellers will begin to self-isolate at home before taking a coronavirus test a week after landing, according to the Telegraph.
The Transport Secretary also ruled out testing on arrival at UK airports and ports.
Mr Shapps reportedly said that the tests will be provided by the private sector and paid for by the traveller to prevent putting extra strain on the NHS.
“We’re also proposing an internationally recognised system, in which Britain would be a trailblazer, where tests and isolation take place prior to travel and after travel and would require no quarantine,” Mr Shapps added.
He said he believed the measures described "will result in significantly more people flying in the months ahead".
But Mr Shapps stopped short of providing a start date for the planned testing scheme.
Mr Shapps earlier insisted that the importance of the travel and tourism sectors is “appreciated and understood by everyone in Government”.
He told the convention: “It’s precisely because the travel industry is so important that we’ve supported it with unprecedented measures across the British economy.
“The furlough scheme… paid up to 80 per cent of employees’ wages, with more than 55,000 staff benefiting within aviation alone.”
He went on: “We’ve been working flat out all summer to try to revive tourism and travel.
“We created those travel corridors, to give families the chance to enjoy a holiday after those months of lockdown.
“But from the very start, we’ve had to be cautious because as we know, new Covid spikes risk wider restrictions down the line and ultimately, even more pain for travel firms.”
On Tuesday, 19,724 more infections were reported and 137 new deaths as Britain's daily Covid-19 cases have jumped 40 per cent in a week.
Department of Health figures show 14,162 cases and 70 deaths were recorded last Wednesday, as well as 17,234 cases and a four-month high of 143 fatalities yesterday.
Last week, Mr Shapps announced the launch of the Global Travel Taskforce.
The group will be jointly chaired by Mr Shapps and Health Secretary Matt Hancock, and will look at how a testing operation could be rolled out.
It will consult with the aviation, travel, healthcare and coronavirus testing sectors, and is expected to make initial recommendations next month.
Mr Shapps also announced that travel from Lesvos, Tinos, Serifos, Santorini and Zakynthos will no longer require self-isolation upon arrival in England and that no countries are being added to the "red list"
The week before, Mr Shapps added Turkey and Poland to the quarantine list as well as the Caribbean islands of Bonaire, St Eustatius and Saba.