The DVLA does not keep figures on the number of road-legal quads, but the main UK suppliers say that since 2005 they have gone from selling a few hundred each year to thousands.
Dr John Heyworth, president of the College of Emergency Medicine, told BBC Radio 1's Newsbeat: "We know that the riders on these quad bikes are at real risk of serious injury and even death because they are seriously unprotected.
"We know from experience that head injuries are the biggest killer in these sorts of accidents.
"So for goodness sake let's protect these riders. It's a simple bit of protection for them that will save lives."
Kevin Clinton, head of road safety at the Royal Society for the Prevention of Accidents (Rospa), supports the call to make it compulsory for riders to wear a helmet on public roads.
"Quad bikes are powerful machines that can reach very high speeds. In the event of an impact, riders are likely to be flung off the bike with the obvious risk of suffering serious injuries," he said.
However, he said, the relatively low numbers involved in serious accidents and the lack of casualty data available, made it difficult to justify spending parliamentary time on this, at the expense of more serious road safety issues such as drink driving.
Quad bike rider Dan Ormesher, 23, told Newsbeat: "Riding them is awesome. It's probably at its best in the sumer weather. All you need when it's nice and hot is a pair of shorts, T-shirt, vest and off you go - it's a buzz.
"I don't think helmets should be worn, but obviously it's up to the people in charge.
"I sometimes wear a helmet, depending on how far I'm going. If I'm staying close, going round town, I won't wear a helmet.
"It's as dangerous as you make it. If you're a safe rider - sensible, aware of what's going on around you - you're more likely to be safe.
"But if you're not - reckless, speeding everywhere - then you're more likely to have an accident."
Glamour model Amii Grove is keen to see helmets made compulsory after she lost her brother, Lee Marley, in a quad bike accident two years ago.
The 24-year-old told Newsbeat: "He had a head-on crash with a Land Rover. He died because of his head injuries.
"So if it was compulsory to wear a helmet, he would probably still be alive today."
There are no separate statistics on the numbers of quad bike crashes, but two particularly high-profile accidents have made headlines and brought the dangers to wider public attention.
In 1998, comedian Rik Mayall suffered serious head injuries and spent five days in a coma after his quad bike overturned while he was riding it at his farm in Devon.
In 2003, rock musician Ozzy Osbourne spent eight days in a coma, broke eight ribs and punctured a lung while riding a quad bike in the grounds of his Buckinghamshire mansion. He was not wearing a helmet at the time of the crash.