The penalty is included in a law that will be voted on by members of Parliament on Thursday.
Outdoor holidays are currently not allowed under the “stay at home” law that expires on Monday.
From next week the ban on leaving the UK will be a specific law, backed by the threat of fines.
Under the current restrictions plan, the first people in England to go abroad for a holiday will be on 17 May.
However, further increases in Covid cases on continental Europe, as well as the slow release of vaccines throughout Europe, have cast doubt on the start of foreign travel.
Health Secretary Matt Hancock said travel restrictions were needed to prevent the importation of large numbers of new cases and variations that could jeopardize drug delivery.
Shadow Cabinet Office Minister Rachel Reeves told BBC Breakfast that the labor force supports measures to keep UK borders safe and avoid the importation of new imported species but said the government's "slow action" has contributed to the country's high mortality rate.
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Prime Minister Boris Johnson warned on Monday that the UK must "not deceive itself" that it will hear the consequences of rising crime on the continent.
One of his ministers, Lord Bethell, said England could put "all our European neighbors" on the "red" list of countries.
However, Mr Hancock told BBC Radio 4 Today's program that there were no plans to do so.
People from those countries are currently not allowed to go to the UK, except for British people and people who usually live in the UK - but those two groups have to pay for isolation from the hotel if they choose to come at the moment.
The "red list" was introduced as part of a tourism policy aimed at establishing a separate Covid entry into the country and being updated regularly, meaning that countries could be added or removed depending on their Covid status.
The work of the international tourism government is considering a coherent or robotic travel plan in place to lift the ban on leaving the country.
The discussion focuses on what constraints might apply to travelers returning from low-lying areas.
The intention is to publish this framework on April 12, with decisions on which standard countries should be taken over time.
Screening for children traveling is considered because coronavirus vaccines are currently not approved for those under 18 years of age.
The new coronavirus laws, which will be unveiled on Monday, suggest that anyone leaving England to travel outside the UK for no apparent reason, such as working, education or medical treatment, could face a £ 5,000 fine.
Anyone traveling abroad must complete a "Travel Outlet" form, stating a valid reason for leaving the country, such as education, employment, or child care.
The travel restriction in England does not apply to those traveling to or from the common tourist destinations of the Channel Islands, the Isle of Man and the Republic of Ireland unless it is not the last resort.
Dedicated UK nations have the power to set their own coronavirus limits.
The first day people in Scotland and Wales will be able to go on holiday abroad, such as England, 17 May, while Northern Ireland has not yet announced its plans.