Boris Johnson has said that people should not be travelling to an amber list country for a holiday.
Countries currently on the amber list i nclude popular tourist hotspots such as Spain and Greece.
On Monday more than 150 flights departed the UK for amber list destinations such as the United States and France.
Environment Secretary George Eustice said people could go to those countries if they observed quarantine rules on their return.
Speaking to BBC Radio 4 he said: "We don't want to stop travel altogether and the reason, as (Health Secretary) Matt Hancock set out, that we have the amber list is there will be reasons why people feel they need to travel either to visit family or indeed to visit friends.
"They can travel to those countries but they then have to observe quarantine when they return and have two tests after returning.
"So people can travel to those areas, yes, but they will then have to subject themselves to the quarantine requirements on return."
But today the Prime Minister said that people should not be travelling to an amber list country unless it was for a vital reason.
Mr Johnson said: "I think it's very important for people to grasp what an amber list country is: it is not somewhere where you should be going on holiday, let me be very clear about that.
"And if people do go to an amber list country - they absolutely have to for some pressing family or urgent business reason - if they have to go to an amber list country, then please bear in mind that you will have to self-isolate, you'll have to take tests and do your passenger locator form and all the rest of it, but you also have to self-isolate for 10 days when you get back.
"And that period of self-isolation, that period of quarantine, will be enforced with fines of up to £10,000 so I think it's important for you to understand what an amber list country is."
Mr Johnson continued: "I think it's very important for people to understand that if you go to an amber list country, if you absolutely have to go for some pressing reason - not a holiday - if you have to go then bear in mind you're going to have to pay for testing, you're going to have to do a passenger locator form, all that kind of thing.
"But you're also going to have to self-isolate for 10 days at home, not going out.
"And if you fail to obey that then you will face fines of up to £10,000.
"People need to understand that an amber list country is definitely not a green list country."
The Prime Minister's official spokesman also insisted this afternoon that travel to amber list destinations was only permitted for a strictly limited number of reasons.
He said that people should still not be going to those countries for holidays or leisure purposes.
The spokesman said: "The position remains that people should not travel to amber list countries and that is to protect public health.
"There are some limited reasons why it might be acceptable to travel - for work purposes, protecting essential services or compassionate reasons such as a funeral or care of a family member - but otherwise people should not be travelling to these countries."
