Online sales run by major supermarkets have come under scrutiny from the Office of Fair Trading (OFT).
Supermarkets deny overcharging online customers
"We are examining supermarket pricing online, and we have held confidential discussions with supermarkets," an OFT spokeswoman told the BBC.
Tesco, Asda and Sainsbury's confirmed that they have held talks with the OFT.
The OFT is believed to be examining whether supermarkets stick to advertised prices, and if online and store prices differ.
Its spokeswoman declined to comment on what the inquiry is looking into, or when it might report.
"Our investigations have no time frame," she said.
According to a report in the Sunday Times, the OFT is questioning online grocers about their practices in at least four areas of concern.
It lists these as higher-than-advertised prices; charging for a premium product and supplying a regular item; higher prices charged for online purchases than in-store items; and whether websites are used to off-load food close to the sell-by date.
Major supermarkets contacted by the BBC denied the allegations.
"We do not 'overcharge' customers", said Tesco group corporate affairs director Lucy Neville Rolfe. Tesco is Britain's biggest grocer.
"With a Tesco.com grocery shop your food is picked off the shelves of your local store so whether it is a book you are buying or a carton of milk, you will be paying the same price as you would instore."
She confirmed that "the OFT contacted the industry several weeks ago on a confidential basis on a fairly technical issue and we will be responding to them".
An Asda spokesman said it has a national pricing system which prevents any variation.
"We only sell products at one price, and it's the same price whether it's in Scotland or Cornwall. We don't have different prices at different stores, and we don't have different prices online".
Ocado, the online shopping service for Waitrose food, which is 43% owned by Waitrose, also sticks to a single national price, its founder and chief financial officer Jason Gissing said.
A Sainsbury's spokeswoman said the group was "in consultation with the OFT" about online shopping, but declined to give further details.