The UK could see a second spike in coronavirus cases if young people don't follow social distancing rules, the health secretary says.
A third of all cases in England last week were people aged between 20 and 29.
"The numbers have been going up. And we've seen in other countries where this leads, and it is not a good place," Matt Hancock says.
Students starting university this month is a "concern", he adds.
Speaking to Radio 1 Newsbeat, the health secretary pointed to France and Spain, "where that second wave started largely amongst younger people, it then spreads".
"And now we're seeing a sharp rise in the number of people in hospital and the number of people who are dying in those countries.
"That hasn't happened here yet. And if people follow the social distancing rules, then we can stop that from happening here."
On Sunday the government announced 2,988 new cases - the highest figure since 22 May, while a further 2,948 were reported in the 24 hours to 09:00 BST on Monday.
The seven-day rate of new cases of Covid-19 in the UK has risen above 20 cases per 100,000 people.
In the seven days to 7 September the rate stood at 21.3 cases per 100,000, up from 13.9 in the previous week (the seven days to August 31).
A rate of 20 cases per 100,000 or above, if reported in other countries, is the level at which the government considers imposing quarantine conditions on people travelling to the UK.
Leeds has been added to the lockdown watchlist. Officials said there had been an increase in music events, house parties and illegal raves in the city.
Meanwhile, up to 300 people who attended a charity football match near Sunderland have been asked to self-isolate for two weeks after 28 people who attended the event tested positive.
And a school in Suffolk has closed after five members of teaching staff tested positive.
The health secretary stressed how serious coronavirus can be for young people, even though they are less likely to die or get seriously ill.
"Long Covid is really serious. And people can be in a bad way for months and months and months," he says.
"The second really important message is that younger people spread the disease, even if they don't have symptoms.
"Don't kill your gran by catching coronavirus and then passing it on. And you can pass it on before you've had any symptoms at all."
The health secretary denied that rules meant to prevent the spread of coronavirus in the UK are unclear.
'Are you willing to risk lives?'
"The rules are really clear, which is indoors you should socialise with only one other household and outdoors with groups of six as a maximum (in England).
"The message is really clear. The question is, how much are you willing to risk the lives of yourself and others by breaking the social distancing rules?"
Some have complained that the government encouraging people to spend money in pubs and restaurants, via the Eat Out to Help Out scheme, and go back into the office, is contradictory to stopping the spread.
But Hancock insists "Covid-secure workplaces are safe", as are pubs and restaurants as long as you "follow social distancing when you're there".
Matt Hancock told LBC areas in the UK that saw a rise in coronavirus cases over the summer were some of the most deprived. But in recent days the rise is among "more affluent younger people".
The health secretary also outlined a new system of testing for people returning from holiday.
He claimed that doing a temperature check at the border - which doesn't happen in the UK but does in other countries - "doesn't work" because the virus can "incubate for a period inside your body without a test being able to pick it up".
Testing people eight days after they have returned is "one of the things we'd like to bring in as soon as it's practical to do it", Hancock said.
It's suggested this could reduce the 14-day quarantine period when returning from countries with a higher number of cases.
Rise in cases 'always likely'
There is understandable concern about the rise in infections that has been seen.
But it needs context - at the peak of the pandemic in spring around 100,000 new cases a day were being seen it is estimated.
Some of the rise seen in recent weeks is down to more testing, but that won't be the only factor.
It was always going to be the case that as people mix more (to go to work and school, not just socialising) and summer ends (respiratory viruses tend to do better in the colder months) cases would go up.
The crucial question is by how much and to what extent will they spill over into older, more vulnerable age groups.
If it can be contained to younger age groups, who are at such low risk of complications, it would in theory not be much of a problem.
But achieving that is going to be difficult.
The social distancing that is now becoming a routine part of our everyday lives and the test and trace teams in place will help.
But sadly hospitalisations and deaths will soon start going up - they do every winter because of flu even though we have a vaccine and some immunity.
Keeping that rise as low as possible - while allowing society to function with children going to school and people being able to work - is the tightrope we will all now need to walk.