Official data showed UK food prices were 19.1% higher in March than a year earlier, the biggest such rise since August 1977, while in April, grocery inflation was 17.3%, according to industry data.
"Given ongoing concerns about high prices, we are announcing the stepping up of our work in the grocery sector to understand whether any failure in competition is contributing to grocery prices being higher than they would be in a well-functioning market," the Competition and Markets Authority said.
It said it would focus its work on areas where people are experiencing the greatest cost of living pressures.
Supermarket groups, including market leader Tesco, deny claims from consumer groups and trade unions that they are profiteering, saying they have taken a hit to earnings and have operating margins of 4% or less, while consumer goods firms such as Unilever and Nestle have margins of 16-17%.
Weakening Retail Competition
Separately, the CMA said it had found evidence that weakening retail competition was contributing to higher fuel prices for drivers.
It said it was not satisfied that some supermarkets had been sufficiently forthcoming in their responses to its road fuel market study.
"So we will be calling them in for formal interviews to get to the bottom of what is going on," CMA CEO Sarah Cardell said.