France’s notoriously reckless drivers often come under fire over its high number of road deaths, but holidaymakers are now facing a new danger: speeding cyclists riding illegally souped-up electric bikes.

The modified e-bikes are terrifying pedestrians and conventional cyclists.

They are capable of reaching 30 miles per hour without pedalling, double the speed limit for electric bicycles in France.

Owners are boosting the power of their e-bikes themselves by following online instructions that explain how to make the relatively simple adaptations required.

The alarm has been raised by Lionel Quillet, the conservative mayor of Loix, on the Île de Ré, a popular family holiday destination where the bicycle is king.

The island off France’s west coast has more than 70 miles of cycle paths although it is only 18 miles long by 3 miles wide.

In summer, about 6,000 bikes a day pass through some sections of the island, many ridden by children.

After a number of accidents, Mr Quillet said souped-up e-bikes should be banned from cycle paths.