The prices of some budget food items have risen by more than 15%, according to new data, with pasta showing the steepest jump over a year.
The lowest cost version of pasta rose by 50% in the year to April, said the Office for National Statistics (ONS).
Household staples such as minced beef, bread and rice also recorded large increases.
But the average price rise of 30 budget food items at supermarkets was 6.7% - below the rate of inflation.
The cost of living, or rate of inflation, rose by 9% in April, said the ONS.
Despite sharp increases in the price of some items such as pasta, the ONS analysis found that the cost of its basket of low-cost groceries increased at a similar rate to the general basket of groceries used for the official measure of food and drink inflation.
Earlier this year, anti-poverty campaigner Jack Monroe criticised large supermarkets for "stealthily" removing value food ranges from their shelves, forcing shoppers to "level up" to higher priced goods.
She criticised the way that the rate of inflation was calculated - which measures the prices of 700 goods - stating that it "grossly" underestimates "the true cost of living crisis".
In this latest data, the ONS measured the price of 30 everyday grocery items across seven supermarkets between April 2021 and 2022.
It showed that the price of crisps rose by 17%, bread and minced beef grew by 16% and rice prices rose by 15%.
Some everyday items showed a drop in prices, led by potatoes which were down by 14%. Cheese, pizza, chips, sausages and the price of apples were also lower.
Measured by price rather than percentage change, minced beef showed the biggest rise, up 32p for 500g to £2.34. It was followed by chicken breast which rose by 28p to £3.50 for 600g.
The price of chicken - the UK's most popular meat - has risen sharply due to a number of factors. According to an analysis by the BBC, higher feed costs and soaring transport prices have contributed to the increase.
Ms Monroe told the BBC: "The figures that are out today will not come as news to anyone who is actually living this because we have all seen the prices of food go up."
She said that having price rises that reflect reality for millions of people shown in official data "puts us in a stronger position to campaign for things like better wages [and] a higher up-rating for benefits".
Following her comments earlier this year, Asda pledged to stock its budget ranges in all of its supermarkets.
"All of the others just held fast and ignored it really," said Ms Monroe on Monday. "If one supermarket could implement the changes, why can't the others?"
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In response, a Sainsbury's spokesperson told the BBC that they understand customers are facing significant pressure on their household budgets.
"We are doing all we can to help, and as part of our plans to focus on offering the best quality food at the lowest prices, today we announced we are investing £500m so that customers will be able to find low prices on the everyday items they buy most often," the spokesperson added.
Meanwhile, Tesco said it is "absolutely committed" to helping customers by keeping a "laser focus" on the cost of the weekly shop.
"We have significantly increased the number of value lines we offer and whether it's price matching around 650 basics to Aldi prices, promising Low Everyday Prices on 1,600 staples, or offering exclusive deals and rewards through thousands of Clubcard Prices - we're more committed than ever to providing our customers with great value," a spokesperson told the BBC.
The BBC has also contacted Morrison's, Lidl and Aldi for a response.
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