The ONS examined the figures after Ms Monroe raised concerns that poorer families were disproportionately feeling the pinch from faster increases in prices of value items.
She said that the official measure of price rises “grossly underestimates the real cost of inflation as it happens to people with the least”.
ONS experimental data found that value range pasta, beef mince and bread jumped at price. The cost of value range potatoes, cheese, pizza and chips fell.
Budget brand pasta was up 50pc in the year to April and value crisps were up 17pc, a faster rate than their more expensive counterparts.
However, these increases were offset by budget products that rose in value more slowly than expensive versions, or fell in price compared to increases elsewhere.
Overall the inflation rate on low-cost items was broadly in line with the average product range, contrary to Ms Monroe’s complaints.
Food price inflation hit 6.7pc in April, compared to 6pc for the 30 budget items tracked by the ONS.
Nonetheless, Ms Monroe claimed victory on Twitter, saying the figures proved it is “far more expensive to be poor”.
She told the BBC News channel: “Almost all of the products had gone up in price and these are… the basics range and value range products.
“They are much higher than the official inflation statistics of 6pc and 7pc, which is what is used to argue for the uprating levels of benefits and what is used as the official inflation figures.”
Some 17 out of the 30 items tracked either rose slower than wider food cost inflation or dropped in price over the period.
In its research, the ONS said: “Highly experimental research, based on web-scraped supermarket data for 30 everyday grocery items, shows that the lowest-priced items have increased in cost by around as much as average food and non-alcoholic drink prices (with both rising around 6pc to 7pc over the 12 months to April 2022).
“There is considerable variation across the 30 items, with the prices for six items falling over the year, but the prices of five items rising by 15pc or more.”
Alongside energy costs, grocery bills have been a key driver of inflation, which has hit a four-decade high of 9pc. Global food prices have soared to record highs in recent months as the war in Ukraine boosts costs from fertiliser, fuel and animal feed.
The ONS’s statisticians said the lowest priced everyday items have “seen a notable variation in price change, with some items showing increases of over 15pc, while other items fell in price”.
The statistics body tracked the price of budget items and how they had changed over the previous 12 months.
The price of a 2.5kg bag of budget potatoes has dropped 12p to 75p, a 14pc slide and the largest fall recorded.
Value cheese slipped 7p to 88p, a 7pc fall, and pizza sank 4p, or 4pc, to 95p.
By comparison the price of potatoes, cheese and pizza rose in price overall when including more expensive ranges, meaning people buying budget versions of these items were comparatively better off.
Earlier this year, Ms Monroe claimed that “margins are always, always calculated to squeeze the belts of those who can least afford it and massage the profits of those who have money to spare”.
Some budget items climbed in price faster than their mid-range counterparts.
The ONS figures suggest budget pasta jumped by 50pc year-on-year in April, a much faster rate than the 10pc increase in the overall “pasta and couscous” category.
Value crisps were up 17pc compared to a 6pc rise for the snack overall.
Budget bread climbed 16pc in price over the 12-month period but the cost of all bread rose just 4.9pc.
Across all items, price rises were broadly the same for budget and mid-range products.