Spall, whose career includes appearances in a string of Leigh's films, ended up taking lessons several times a week in preparation for the role in Mr Turner.
Speaking at a press conference at the Cannes Film Festival, he said Leigh sent him away to get art lessons.
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He told reporters: "He said 'right we're going to make this film in two and a half years time, I'd like you to start painting'. So I started to learn how to paint two years before I started rehearsing then we rehearsed six months.
"A brilliant English portrait painter called Tim Wright gave me lessons, when I wasn't working I'd see him two or three times a week."
Spall said his physical similarity to the legendary painter also helped, saying: "What made us the perfect match more than anything was he was a funny-looking fat little man and so am I".
The film's producer, Georgina Lowe, revealed they could not film scenes set in Margate because the view from the town had changed since a gallery named after Turner was built there.
The Turner Contemporary, which is on the site of a guest house where Turner stayed which features in the film, opened its doors in 2011.
Ms Lowe said: "We didn't go to Margate because of the gallery that's in the situation there now and it's completely changed and we quite simply found a beautiful location in Cornwall."
Leigh said: "Some people who really know Margate will object to that fact, that the Margate in the film really doesn't look anything like Margate but this is our distillation of Margate and I think it serves the needs of the film".
Leigh's film is one of 18 movies in the running to be awarded the Palme d'Or - the prestigious prize handed out every year to the best film in competition at the annual event in the south of France.