Coronavirus restrictions were tightened in the Scottish city of Glasgow and extended in parts of northern England on Wednesday following a surge in infection rates.

The new measures come amid a steady uptick in cases across Britain, which has suffered Europe's deadliest outbreak of Covid-19, with more than 41,500 confirmed deaths.

Regional restrictions imposed on the towns of Bolton and Trafford in England's Greater Manchester area were due to be lifted on Wednesday but at the last minute they were prolonged.

Local politicians had called for a continued ban on social gatherings in homes and private gardens, with Manchester mayor Andy Burnham advising the public to ignore any relaxing of the rules.

But in a statement released just as the restrictions were due to be lifted, Health Secretary Matt Hancock said they would stay.

"We continually monitor outbreaks across the country and have seen infection rates increase more than three times in Bolton in under a week, and double in Trafford since the last review," he said.

"We have always been clear we will take swift and decisive action where needed to contain outbreaks."

Restrictions were however lifted as planned in other areas of north and northwest England Wednesday, including Burnley, Hyndburn, Stockport and parts of Calderdale, Kirklees and Bradford.

Elsewhere, the devolved government in Scotland reimposed restrictions on Glasgow and two surrounding areas, warning against visiting other people's houses.

The measures, which will last two weeks, came after 66 new cases were recorded in the area on Tuesday.

Scottish First Minister Nicola Sturgeon -- herself a Glasgow resident - acknowledged "how difficult this would be" but said it was "essential to, I hope, nip this in bud and avoid tougher restrictions".

On the city's streets, many people accepted the new measures were necessary -- but questioned how they would be enforced.

"It's probably for the best in the long scheme of things. I'm just not sure how successful it's going to be," Rachel Hutton, a 20-year-old tour guide, told AFP. 

"I feel like it's going to be quite hard to enforce. But I hope it's for the best and I hope it keeps people safe more than anything else."

Nationwide restrictions were imposed in Britain in late March, but the lockdown has since been largely lifted, with localised restrictions introduced to deal with flare-ups.

Separately, Scotland announced that anyone arriving from Greece from Thursday morning would have to self-isolate for two weeks, after a "significant rise" in imported cases.

Greece is currently on a safe list for travellers entering England, but the policy is reviewed every week.