Police and contractors are to go door to door checking that people who have returned from holiday are quarantining - and handing out fines of up to £10,000 in England.
Home Secretary Priti Patel says enforcement will be stepped up and people who aren't quarantining after visiting a country on the amber list will face action.
In Scotland, anyone returning from an amber-list country must complete a passenger locator form, take a Covid-19 test on arrival in the UK, book and pay for two more tests to be taken on days two and eight and isolate at home for 10 days.
It is unclear if Police Scotland will follow suit north of the border.
Ms Patel has authorised enforcement after non-essential international travel was permitted again on Monday, reports The Mirror.
Private contractors will visit up to 10,000 homes a day checking that people are complying with the rules - those who don't will get a visit from the police.
More than 27,000 people are expected to have gone to an amber list country by Sunday.
Ms Patel told the Daily Mail : "People will not go unchecked. Significant resources have been put in place – millions of pounds – in terms of the follow-up checking of people around their testing and making sure they stay at home. It has been stepped up."
At Wednesday's Downing Street briefing, England's Health Secretary Matt Hancock said the UK government had been "absolutely crystal clear" that people should not go to amber list countries.
"If you look at what the PM said last week, what I said at the weekend, what I said in the House on Monday, what the PM said at lunchtime today - we've been absolutely crystal clear," he said.
"You should not go to an amber or red list country on holiday. You should only go in exceptional circumstances."
He suggested as examples that you could travel to "visit a very ill family member" or to "go to a funeral".
Mr Hancock said even though there are some things the Government doesn't advise doing, "you don't necessarily have to ban everything by law."
The Scottish Government has been contacted for comment.
