Tesco, Morrisons and Waitrose are among the supermarket chains to issue to new due to problems with the UK's supply chain.
The issues, that have come about due to Russia's invasion of Ukraine, had led the leading shops to place limits on how much cooking oil customers can buy in one go.
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Of the three, Tesco is allowed three items per customer while Waitrose and Morrisons have placed limits of just two items each, according to the BBC.
In comments carried by the broadcaster, the British Retail Consortium's (BRC) Tom Holder said the move was a temporary measure "to ensure availability for everyone".
Richard Walker, managing director of Iceland supermarkets, said his shops were having to ration sunflower oil sales to one bottle per customer, reports LiverpoolEcho.
He told BBC Radio 4's Today programme: "It is not as frenzied as the toilet roll panic buying from a couple of years ago, and we are managing to maintain an offer. But yes, we are limiting purchases and we've moved into smaller packs to allow existing stocks in the market to service more customers."
Most of the UK's sunflower oil comes from Ukraine, with the restrictions applying to that product as well as olive and rapeseed oils at some supermarkets. Mr Holder from the BRC said retailers were "working with suppliers to ramp up production of alternative cooking oils, to minimise the impact on consumers".
Recent data showed cooking oil was one of a range of food staples to have its price shoot up. The price of cooking oils and fats went up 7% and is nearly a quarter more expensive than a year ago, the Office for National Statistics said on April 13.
Iceland boss Mr Walker told Today: "If you look at commodity prices, sunflower oil has gone up 1,000% in terms of the commodity cost in the market, palm oil (up) 400 per cent and then there is things like wheat, 50 per cent, fertiliser, 350 per cent. These are all unintended consequences of the war in Ukraine that is affecting supermarkets."
Tesco said in a statement: "We have good availability of cooking oils in stores and online. If a customer is unable to find their preferred oil, we have plenty of alternatives to choose from. To make sure all of our customers can continue to get what they need, we've introduced a temporary buying limit of three items per customer on products from our cooking oil range."
A Sainsbury's spokesperson said they have no plans to introduce limits.
