Government ministers are pressing supermarkets on cutting costs for shoppers but will not force them to cap prices on essentials such as eggs, bread and milk.

Multiple supermarket sources told the BBC that the government had urged them to voluntarily freeze the price of key groceries, in return for an easing of regulations.

On Wednesday, Treasury secretary Dam Tomlinson confirmed talks with the sector had taken place "about the steps that they can take to support people with the cost of living".

He said supermarkets would not be forced to cap prices, but even a voluntary scheme was described by former chairman of Ocado and Conservative peer Lord Rose as the "stuff of nonsense".

The BBC learnt on Tuesday that the Treasury had asked retailers to freeze price rises on certain products in exchange for an easing of packaging policies and a potential delay to rule changes around healthy food.

The proposals, first reported by the Financial Times, come after the Scottish National Party (SNP) pledged to introduce a similar policy in Scotland last month. However, its price cap would not be voluntary.

Tomlinson told BBC Radio 4's Today programme there were no plans to instil a mandatory price cap on food by the government in Westminster.

Pressed on a voluntary agreement to limit prices, Tomlinson highlighted the conflict in Iran and people's concerns over price rises.

"It's right that the government looks across the board at what more we can do - both government levers but also talking to industry about the steps that they can take to support people with the cost of living," he said.

Newly-published inflation figures show the annual rate of food price rises was 3% in April, which was higher than the overall rate of inflation of 2.8%.

Some industry groups have warned the rate of food price rises could hit nearly 10% by the end of the year.