Whites in Beverley, which appears in the Good Food Guide, confirmed today that two groups of four had cancelled their bookings for meals at the restaurant as they did not have enough petrol left to travel there.
The restaurant, which offers a tasting menu, has just 16 covers and is run by chef John Robinson, who has owned the business for 13 years.
He tweeted earlier: "Completely understandable but just another example of the very weird times we are living in."
Meanwhile, holiday accommodation provider Runswick Bay Cottages, run by Helen Massey in the popular village near Whitby, reported queries from guests with bookings they feared they would be unable to take up.
She said: "Someone has asked me what my policy is if they can’t get to the cottage because they can’t fill up with petrol for the journey. Can someone stop the world…..I’d like to get off please!"
Many forecourts in Yorkshire are now closed following long queues after customers mistakenly believed petrol supplies could run out.
Fuel providers have insisted the crisis has been blown out of proportion, and that only a small number of petrol stations were initially affected by a shortage of lorry drivers which slowed down delivery times.