University students must be allowed to return home to their families at Christmas, Labour has said, amid fears that coronavirus outbreaks could keep young people in halls when term ends.

Thousands of students are currently confined to their rooms following a surge in cases at institutions including Glasgow, Manchester Metropolitan and Edinburgh Napier.

Health Secretary Matt Hancock last week declined to rule out asking students to stay on campus over Christmas, after Government scientific adviser Sir Mark Walport said the measure may be needed to stop the virus spreading to older relatives.

Shadow education secretary Kate Green has written to her opposite number Gavin Williamson, urging him to “promise” students that such restrictions will not be imposed.

She said it would be “deeply unfair to see students forced to remain in their student accommodation” and asked Mr Williamson to “work with universities to ensure every student has access to testing to allow a safe journey home” for Christmas.

Ms Green also asked the Education Secretary to consider a delay to the start of term or a “pause in migration” for universities where term has not yet begun to allow improvements in testing capacity and remote learning provisions.

In a statement, she said: “Leaving home to go to university should be a momentous and exciting step for young people and their families. Universities have done all they can to prepare for students’ safe return, but the Government has again let young people down.

“It is unthinkable that students will be locked in their rooms and unable to return home to spend Christmas with their families. The Government must promise that this will not happen, and work with universities to enable every student to access tests so that they can travel home safely.

“The Government should also consider a delay to the start of term or a pause in migration for universities where term has not yet begun to allow improvements in testing capacity and remote learning provision.

“Gavin Williamson must urgently come to Parliament and set out how he will resolve the critical situation in our universities that is causing such anxiety for families across the country.”

A Department for Education spokeswoman said: “The Government is working closely with universities to ensure they are well prepared for the return of students, and we have published guidance to help them keep students and staff as safe as possible.

“Students should follow the latest health advice, just like the wider public, which means they should stay at university in the event that they have symptoms, have to isolate, there are additional restrictions imposed locally, or there is an outbreak on campus or in their accommodation.

“We will continue monitoring the situation very closely and follow Public Health England advice, adapting policies to best support students and providers.”

Glasgow University said on Saturday that it will refund all students in halls of residence one month’s rent, along with a £50 payment for food, after the outbreak of cases.

In other developments:

– An issue preventing users of the NHS Covid-19 app in England logging a positive test result has now been resolved, but people who book a test outside the app still cannot log negative results.

– There were a further 6,042 lab-confirmed cases of coronavirus in the UK as of 9am on Saturday, taking the overall number to 429,277. A further 34 deaths were recorded.

– Thousands of protesters gathered for an anti-lockdown demonstration in central London on Saturday, with none appearing to wear face coverings or to social distance.

– Tory backbenchers said they would continue to push the Government to give MPs a chance to debate and vote on coronavirus measures before they come into force despite Downing Street’s attempt to head off a rebellion. Former minister Steve Baker wrote in the Telegraph that Parliament “must take back control”.

– Frontline workers who played a key role in the coronavirus pandemic response will be recognised in the Queen’s Birthday Honours next month, the Prime Minister said.

More than 17 million people – a quarter of the UK population – will be under tougher coronavirus restrictions later on Sunday as new measures are introduced in Cardiff and Swansea at 6pm.

People will not be able to enter or leave the areas without a reasonable excuse. They will not be able to meet indoors with anyone they do not live with, with extended households suspended.

Bans on households mixing came into force in Wigan, Stockport, Blackpool and Leeds on Saturday, while stricter rules are already in force across large swathes of north-west England, West Yorkshire, the North East and the Midlands, as well as parts of west Scotland.

A ban on households mixing indoors was extended across Northern Ireland earlier this week.