Alastair, who was dubbed the 'Godfather of modern British cooking', rose to fame in the 1980s when he opened his self-named restaurant in Soho.
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The establishment was famed for its simplicity, serving soup, salad, fish, meat and puddings, with the menu usually changing throughout the day based on the supply of ingredients.
He also appeared on various TV shows including Ready Steady Cook alongside James.
The 50-year-old chef took to his Instagram page to express his shock over the heartbreaking news, writing: "So sad to hear the news one of the true godfathers of British food has passed away.
"I had the honour of first meeting Alastair Little at college as a young kid and later doing stints at Frith Street which was a Mecca for all foodies at the time... later on Ready Steady Cook and beyond.
James shared this snap of Alastair Little
"The man was a legend in so many eyes and mine and my thoughts go to his family and friends. Chef, you are and always will be a legend to me and many others. RIP."
Fans were quick to offer their support, with one writing: "Sorry to hear that James you have lost quite a few fellow chefs recently. Please slow down a bit enjoy what you have worked so hard for. Take it easy fella."
Another said: "Omg, such sad news and one of the legends." A third post read: "I was fortunate enough to dine a few times at his Soho restaurant and it was always a total delight. RIP."
Fellow chef Jamie Oliver also mourned the loss of Alastair, who had inspired Jamie with his own cooking. "Rest in Peace Alastair Little," he wrote. "A wonderful chef who inspired me greatly as a young chef, he was just brilliant! Much love to his family. Jamie xxx."