The penalty is included in legislation that will be voted on by MPs on Thursday.
The new law states that no one can “leave England to travel to a destination outside the UK , or travel to, or be present at, an embarkation point for the purpose of travelling from there to a destination outside the United Kingdom” without a reasonable excuse.
Fines of £5,000 can be issued to those who break this rule, according to the regulations.
Foreign travel for a holiday is already illegal, but the punishment is a new measure.
A £200 fixed penalty notice can already be issued to those who fail to fill in a travel declaration form, which includes personal details and reason for travel, for those leaving the UK.