In comments carried by the broadcaster, the British Retail Consortium's Tom Holder said the move was a temporary measure "to ensure availability for everyone".
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 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.
The Russian tanks and missiles besieging Ukraine are also threatening the food supply and livelihoods of people in Europe, Africa and Asia who rely on the vast, fertile farmlands of the Black Sea region known as the "breadbasket of the world".