More than a million people in the UK live in “food deserts” – neighbourhoods where poverty, poor public transport and a dearth of big supermarkets severely limit access to affordable fresh fruit and vegetables, a study has claimed.

Nearly one in 10 of the country’s most economically deprived areas are food deserts, it says – typically large out-of-town housing estates and deprived inner-city wards served by a handful of small, relatively expensive corner shops.

Public health experts are concerned that these neighbourhoods – which are often also “food swamps” with high densities of fast-food outlets – are helping to fuel a rise in diet-related conditions such as obesity and diabetes, as well as driving food insecurity.

The most deprived areas include Marfleet in Hull, Hartcliffe in Bristol, Hattersley in Greater Manchester, Everton in Liverpool and Sparkbrook in Birmingham. Eight of Scotland’s 10 most deprived food deserts are in Glasgow, and three of Wales’s nine worst are in Cardiff.

The study, by the Social Market Foundation thinktank and food company Kellogg’s, says poor, elderly and disabled people are disproportionately affected, as they cannot afford or are physically unable to travel to large supermarkets.

Food deserts are defined by the report as neighbourhoods of between 5,000-15,000 people served by two or fewer big supermarkets. In “normal” areas of this size there are typically between three and seven large food stores, it says. Small shops are less likely to sell fresh or healthy food.

The report cites Lisa Cauchi, a mother of eight in Salford, in the north-west of England, who said the nearest reliable source of affordable fresh fruit and vegetables was a big supermarket half an hour’s walk away. She occasionally gets a taxi but finds that depletes her food budget. “A taxi is a meal,” she said.

A survey carried out as part of the study found that nearly a third of respondents reported that lack of money was the biggest barrier to eating healthily (29%), followed by lack of time to cook (22%). Some 18% said they did not know how to cook healthy meals.

“Everyday food insecurity is on the rise in neighbourhoods across the UK. For those living in a food desert this can mean having to dedicate a portion of an already stretched budget toward transportation costs in order to secure food,” said Megan Blake, a food security expert at the University of Sheffield.

Almost 4 million children in the UK are estimated to live in households that would struggle to afford to buy enough fruit, vegetables and other healthy foods to meet official nutrition guidelines, according to the Food Foundation. Food prices rose by 7.7% between 2002 and 2016, while incomes for the poorest families fell by 7.1%.

A Cambridge University study published last year found that people on low-incomes who live furthest from their supermarket were more likely to be obese that those who lived close by. It concluded that improving access to supermarkets for the least well-off – as well as raising their incomes – would help cut obesity.

Some states in the US have experimented with so-called “supermarket solutions” – offering loans and grants to big food stores to attract them into deprived areas as a way of increasing the availability of cheap, healthy foods.

Anna Taylor, chief executive of the Food Foundation, called for urgent action by local authorities and central government to tackle the problem. “If you’re in the poorest 20% of households you need to spend 42% of your disposable income after housing costs to afford the government’s recommended diet. Compound this with transport costs to get to a food shop and a healthy meal is even further out of reach.”

A government spokesperson said: “We are determined to support households to eat healthily … We support 1.1 million children with free school meals and 300,000 pregnant women, families and children under four with Healthy Start vouchers for free fruit, vegetables and milk.

“We are also investing £15m to increase the amount of surplus food from retailers and manufacturers redistributed to charities and community groups every year.”