A quarter of England’s most important A-roads have electric car charging “cold spots”, according to government figures that suggest significant gaps remain in the infrastructure needed to switch away from fossil fuels.

Twenty-nine out of 107 A-roads that are part of the strategic road network have at least one cold spot, according to data obtained by charging company Zest from the Department for Transport. Cold spots are defined as points where a vehicle with only 10% of its battery remaining would not be able to reach a site with at least six rapid or ultra-rapid devices.

Affected roads range from the A1 north of Peterborough, to the A11 south of Norwich, and several parts of the A38 and A42 north of Birmingham.

Several of the cold spots are on vital routes for holidaymakers – who are likely to be the most reliant on top-ups from rapid chargers. They include the A2 on the way to Folkestone, a popular connection to Europe via the Channel tunnel, a huge swath of the A31 and A35 between Southampton and Weymouth, and several parts of the A303 and A30 that are often filled with families on their way via Exeter to Cornwall for summer holidays.

The Lake District is also badly served, with the A590 to the south of Cumbria one of the biggest cold spots. The largest cold spot is the A49 running through Hereford and Shropshire.

The number of public electric car chargers in the UK is rising faster than the number of electric cars, as companies race to snap up the best spots. There were 75,675 public charge points at the end of February, up by nearly a third compared with a year earlier, according to data company Zap Map.

Neveretheless, the rollout has been uneven across the country, with wealthier areas favoured because richer drivers are more likely to own electric cars.

Robin Heap, Zest’s chief executive, said that while the UK was making excellent progress overall on installing more chargers, the government should also look at addressing densely populated areas without many chargers.

He said: “The reality is that most people need convenient access to charging at or near their homes or workplaces to make the switch to electric vehicles.

“It is also worth considering whether public funds, such as the £950m rapid charging fund, which currently supports commercially viable motorway service areas, could be more effectively directed towards cold spots on A-roads and local charging solutions for communities that may never attract commercial investment.”

Companies have rushed to install chargers on the UK’s motorways, because the demand for ultra-rapid speeds means customers are willing to pay higher prices. But A-roads in some parts of the country have received less attention, in part because they may not be as lucrative.

There is also a problem installing chargers on some parts of the road network – even in busy areas – because of a lack of heavy-duty connections to the electricity grid at service stations that can be far from built-up areas.

A Department for Transport spokesperson acknowledged there was more to be done, but said the UK was “making great progress, with over 5,250 rapid and ultra-rapid chargers available within just one mile of our strategic roads – a more than 50% increase in a year”.