Four in 10 Brits say that rules requiring people to wear face masks in shops and on public transport should stay in place permanently – even if the coronavirus pandemic is over.
Almost one in five said they back a permanent 10pm curfew, whether or not there is any risk from COVID.
The results of the poll were branded "total lunacy" by Conservative MP Simon Clarke.
Research by Ipsos MORI found seven in 10 people wanted face mask rules to continue for a month after July 19 - the current scheduled date for the end of mandatory mask requirements and most other restrictions in England.
Slightly fewer people (64%) want to see mask rules on public transport and in shops stay in place until the pandemic is under control worldwide, which may still be years away.
The figure drops to four in 10 when asked if people want the rules to stay forever.
The government has been criticised for its decision to include an end to mask wearing rules when England enters step four.
Watch: COVID-19: Trains, planes and buses can have their own face mask rules after 19 July, transport secretary says
Dr Chaand Nagpaul, chair of the Council for the British Medical Association, said: "We know that masks are effective in stopping the spread, so it is nonsensical and dangerous for the government to abandon compulsory mask-wearing in indoor public settings, such as public transport, on July 19."
Labour has also called for mask-wearing in shops and public transport to be mandatory for the time being.
Sir Keir Starmer pointed out at PMQs on Wednesday there are many people with weakened immune systems who will feel scared about going on public transport if everyone isn't wearing a mask.
He said: "We should open up in a controlled way, keeping baseline protections such as masks on public transport, improving ventilation, making sure the Track and Trace system remains effective, and ensuring proper payments for self-isolation."
The science around how effective masks are at reducing infection is still debated, although it is generally agreed wearing a face-covering does cut cases in some way.
In minutes released by the Scientific Advisory Group for Emergencies (SAGE) recently, they said they had medium confidence that using effective face-coverings reduced infections by between 6-15% – and that the figure could be as high as 45%.
The Ipsos study also found around seven in 10 Brits believed quarantine rules for people returning from a foreign holiday should stay in place for a month after July 19 and a third would be happy for the rule to be permanent.
Almost half of the respondents said they would support vaccine passports becoming a necessity for foreign travel forever.
Two-thirds of Brits supported social distancing rules staying in place for a month after 19 July and over a third said they wanted social distancing forever.