Travellers who break the proposed 14-day quarantine rule will be subject to 'unlimited fines' under tough new measures being put forward by ministers.
Those who flout the rules could face penalties of up to £10,000 under emergency laws to prevent a second outbreak, according to reports.
It comes as ministers prepare to unveil new travel guidelines that could allow passengers to visit low-risk destinations from early summer.
Under the measures, those who arrive in the UK will have to self isolate for two weeks, and in some cases provide a residential address at the border.
It follows a drop in coronavirus cases in the UK - which has claimed almost 35,000 lives in England, Wales and Scotland.
The Government is currently looking at introducing so-called "travel bridges" between countries with low infection rates.
Everyone who comes into the UK will have to isolate for a fortnight under Government plans, which are set to begin in June.
And on Monday night it was reported those who breach the quarantine rules face fines ranging from £1,000 to £10,000.
Ministers are even considering "unlimited fines" for persistent offenders, according to the Daily Telegraph.
"We want to send a very clear message to discourage people from breaching quarantine," one unnamed Whitehall source was quoted as saying.
Only tourists from the common travel areas - like Ireland, Guernsey and Jersey - would be exempt.
And a "very limited" group of up to 30 professions would also be free of the restrictions.
It's reported that would include thousands of lorry drivers bringing food, medicine and vital supplies into Britain.
Diplomats, defence personnel, specialist engineers, some police and customs officers and North Sea oil rig workers would also be exempt, it's reported.
Shapps said in the House of Commons: "The final details of the quarantine scheme will be released soon, coming in early next month."
"It is the case that we would indeed consider further improvements for example, things like air bridges, enabling people from other areas and countries who have themselves achieved lower levels of growth virus infection, to come into the country."
The idea of travel bridges to areas of low infection will give Brits a boost that if our rate of infections continues to fall, they may be able to jet off on a getaway in the coming months.
It is being discussed by the DoT after airline bosses slammed the strict quarantine requirements, warning it would kill the industry.
The boss of Ryanair, Michael O'Leary, has already slammed the proposed 14-day rule, describing it as "idiotic".
Speaking to the Today programme, he said: "It's idiotic and it's un-implementable. You don't have enough police in the UK."
O'Leary said that the policy had "no credibility" and predicted that it would be gone by June.
UK airports have also suggested that a quarantine "would not only have a devastating impact on the UK aviation industry, but also on the wider economy".
Karen Dee from the Airport Operators Association, which represents most UK airports, said the measure should be applied "on a selective basis following the science" and "the economic impact on key sectors should be mitigated".
