But drivers in other areas are charged up to £4 per hour.
To charge a typical electric vehicle (EV) from flat to full at that rate would cost £240, the analysis found.
It would cost around £3.90 to fully charge the same car at home using a dedicated off-peak EV tariff.
EV drivers without a driveway or off-street parking often rely on public charging points.
Drivers in the South generally have access to more devices but have to pay more to use them, the research found.
The average cost per kWh at the cheapest charging points across East Anglia, London, the South East and the South West is 32p, compared with 25p in the Midlands, the North East, the North West, Yorkshire and the Humber and Wales.
The figures were obtained following Freedom of Information requests to more than 400 councils.
Those offering free charging include Bridgend, Leeds and Woking.
British Gas issued a warning over the “postcode lottery” of fees after commissioning a survey of 2,000 motorists, which indicated one in three are nervous about switching to EVs due to charging costs.
The energy firm’s head of EV enablement, Lucy Simpson, said: “The latest figures released today demonstrate the need for all UK councils to play their part in supporting the transition to electric vehicles.
“Currently, we have 21 progressive councils that have decided to support local EV adoption, so we would expect a greater uptake of EVs to come through in these areas than in councils where it is expensive to charge.
“If charging doesn’t become more accessible in these areas, we could see a slower rate of adoption.
“Whilst the Government does offer certain financial incentives at the point of purchase, charging costs are still a barrier to electric vehicle adoption.”
She added: “It’s unfair that those who don’t live in areas with either free or low-cost charging are being discriminated against based on their address.
“If this continues, we risk leaving a huge number of drivers behind in the transition to electric cars.”
The 21 councils which offer free EV charging are:
2. Bracknell Forest
4. Bridgend County Borough Council
7. East Riding of Yorkshire
13. Oadby and Wigston
19. Tunbridge Wells
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