Scotland imposed fresh restrictions on the city of Glasgow on Wednesday after a rise in coronavirus cases, as similar local-lockdown measures elsewhere in Britain came under criticism.

Scottish First Minister Nicola Sturgeon said people living in Glasgow and two surrounding areas should not visit other people's houses, after 66 new cases were recorded in the area on Tuesday. The measures will last two weeks.

"I know how difficult this will be -- I am a Glasgow resident so these rules apply to me too. But they are essential to, I hope, nip this in bud and avoid tougher restrictions," she tweeted.

Nationwide restrictions were imposed in Britain in late March following a surge in cases of Covid-19. Since then more than 41,500 people confirmed to have the virus have died, the worst death toll in Europe.

The lockdown has since been largely lifted but localised restrictions have been introduced to deal with flare-ups.

However, Andy Burnham, mayor of Manchester in northwest England, blasted the approach in his city as "completely illogical".

"Overnight we've had restrictions released in two boroughs where we've got a rising number of cases... and neighbouring boroughs are still under restrictions but with much lower numbers of cases," he told BBC radio on Wednesday.

Burnham, a member of the opposition Labour party, said: "These restrictions were always hard to explain to the public but they are completely illogical now."

David Greenhalgh, the Conservative leader of the local authority in Bolton, which falls within the Greater Manchester area, called for restrictions there -- banning  people from different households from meeting indoors -- to remain.

He said he supported lifting the measures when virus rates were low, but added: "There has been a sudden and unforeseeable rise in the number of coronavirus cases in Bolton."

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

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