It was banned from state schools nearly a quarter of a century ago, following decades of campaigning, amid claims of brutality and barbarism.
But a TES-commissioned YouGov poll shows that almost half of parents now want to see corporal punishment revived.
Even more surprisingly, nearly one in five (19 per cent) of pupils agree that this ultimate sanction should be available to teachers dealing with "very bad behaviour".
The majority of teachers are unlikely to be so keen - separate TES research in 2008 found 73 per cent opposed the re-introduction of corporal punishment even for "extreme cases".
Association of School and College Leaders general secretary Brian Lightman said he was shocked that so many parents back the cane's return. "A lot of them might have said yes, thinking it would be for other people's children," he said. "I wonder what they would say if it was for corporal punishment for their own?"
Nevertheless, the YouGov survey shows that most parents want teachers' classroom powers bolstered and think the profession should have greater freedoms. Only 36 per cent of parents said that teachers' pensions and pay should be subject to cuts.
The YouGov survey, of a representative sample of more than 2,000 parents, suggests the vast majority are already very supportive of teachers.
An overwhelming 91 per cent of parents agreed that teachers should be allowed "to be tougher when it comes to discipline", but almost as many - 86 per cent - are concerned that teachers are "now more fearful of the parents of their pupils".
Nearly two-thirds of parents thought it was unacceptable for parents to criticise teachers in front of other people and 93 per cent thought that "teachers need to have more authority in the classroom".
Their views seem very much in line with those expressed by Westminster Education Secretary Michael Gove in response to the riots in England: "The only way to reverse this dissolution of legitimate authority is step-by- step to move the ratchet back in favour of teachers.
"We need to ensure, in everything we do, that we send a single, consistent, message that teachers are there to be respected, listened to, obeyed."
But where many parents part company with Mr Gove is on exactly what form this authority should take. The poll showed that 49 per cent of parents agree that: "Corporal punishment, such as the cane or slipper, should be reintroduced for very bad behaviour."
And a quarter of parents said they strongly agreed, putting them in direct conflict with the Government, which says it will never bring back the cane.
Peter Newell, co-ordinator of the Children are Unbeatable! Alliance, a coalition of around 1,000 groups including the major children's charities, said: "All European states have prohibited school corporal punishment, some more than a century ago.
"This is not an issue about parents' views - it's about children's protection."
Parental support for the cane is higher among men, at 58 per cent, than women, at 40 per cent.
There are also regional variations, with support highest in Yorkshire, where the return of corporal punishment is backed by 56 per cent of parents, compared with just 32 per cent in the north of Scotland.
Mr Newell argued that the UK's human-rights obligations make corporal punishment a "dead issue", while Mr Lightman said "the days of corporal punishment are long gone".
A Department for Education spokesman said: "There is no intention of ever reintroducing corporal punishment."
Caning: Parental support
Other sanctions supported by parents
90% of parents fear teachers are worried by the threat of legal action when disciplining children
86% of parents think teachers need to gain more respect from their pupils to discipline them properly
33% of parents and
15% of pupils see academic rigour as one of the most important teacher qualities.