The government re-introduced the measure on Tuesday following the discovery of a new, more infectious mutation of Covid-19, called the Omicron variant.
Some 14 cases of the Omicron mutation have so far been found across the UK, although experts expect this number to rise in the coming days.
In Cosham, there was little reluctance from shoppers not to wear masks while picking up their weekly groceries.
Mask-wearing Vera Theseiro, of Cosham, was out shopping with her daughter having just received her coronavirus vaccination booster jab.
The 88-year-old said: ‘We still need to be careful. People should be wearing their masks. It's better to be safe and not sorry.
‘I think especially going into shops, you should still wear them. I don’t care what people say, I will still be wearing mine to protect myself and others.’
Not everyone in Cosham High Street was convinced by the reintroduction of compulsory face coverings in shops.
One 73-year-old of Drayton, who asked not to be named, said he was ‘sceptical’ about the effectiveness of masks and of the whole virus.
The retired science teacher, who said he was an ‘anti-vaxxer’, told The News: ‘I’m reluctantly wearing a mask to show I’m complying with the rules. But I don’t think they’re of any use.’
However, 55-year-old Alister Cross, of Paulsgrove, was firmly in support of mask wearing and had strong views about those who chose to ignore the rules without a valid exemption.
‘We should all be like the Japanese and just wear the damn things,’ he said. ‘Some people need to get over themselves – that’s the biggest problem we have.
‘I don’t like the mentality of people who don’t want to wear a mask, I think there’s a lot of arrogance and ignorance behind it.
‘It’s not hard to wear a mask – I have worn mine ever since this began; every time I’ve gone into the shops or builders merchants I wear it. It’s not hard.’
The news came as concerns continue to mount about the possible impact of the new variant on Christmas plans this year.
Dr Jenny Harries, head of the UK's Health Security Agency, last night urged people to cut back on unnecessary socialising, saying reducing social visits even by ‘a little bit’ will ‘help to keep the virus at bay’.
Prime minister Boris Johnson was asked if he agreed with Dr Harries’s view and whether or not he felt Christmas parties should be cancelled.
He replied: ‘So the answer is no. The guidance remains the same, and we’re trying to take a balanced and proportionate approach.
‘We’ve got the measures in place to fight Delta, which we think are appropriate, and then we’re bringing in some tougher measures to stop the rapid seeding of Omicron in this country to give us the time we need to get the boosters in and of course to find out more.’