Fact check: is chicken tikka masala actually Indian, not British?

While Britain may lay claim to chicken tikka masala, the dish’s origins can be traced back 5,000 years ago to India, says Ashutosh Bisht, restaurant manager of Bombay Dreams in Hong Kong
We all think we know the story.
While the dish has only been around since the 1960s the origin of the dish has a much longer history
The scene: An Indian restaurant in 1960s Britain, not long before closing. Most dishes are already sold out.
The players: A hungry British man and a Bangladeshi chef (at the time, most of Britain's Indian restaurants were owned and run by Bangladeshi chefs.)
The conversation: “Excuse me,” says the man to the chef. “This chicken tikka is a bit dry, can you please bring something else, something better than this.” Wanting to please his customer, the chef returns to the kitchen. Looking around he spies a can of tomato soup and has either a light bulb moment or a moment of desperation. He warms the soup, throws in some spices and a dollop of yogurt and pours it over the chicken.
He presents the dish to his customer, who is thrilled with the result, returning again and again for what is now one of the UK’s most popular dishes, chicken tikka masala.
Or so the legend goes.
The dry chicken and tomato soup tale is, according to Ashutosh Bisht, restaurant manager of Bombay Dreams in Hong Kong, the commonly held belief about the origin of the dish. “It is a story I have heard many times, it is folklore.”
There are a number of variations on the above story, however all agree that its beginnings were accidental improvisation. Only one person has claimed to have known the chef in question.
Asif Ali told the tale on a 2013 episode of British TV cookery programme, Hairy Bikers. His father, Pakistani chef Ali Ahmed Aslam, was the proprietor of the Shish Mahal restaurant in Glasgow.