British leaders, tennis chiefs and former players on Tuesday hailed Andy Murray's grit after the Scot became the first British man to win a Grand Slam since 1936.

Murray was offered the freedom of his local city, as British Prime Minister David Cameron said his five-set defeat of Serbia's Novak Djokovic in the US Open final was continuing Britain's "golden summer of sport" following the Olympics and Paralympics.

"I'm absolutely delighted for him. It is a huge achievement," Cameron said outside his 10 Downing Street office.

"Seventy-six years Britain has waited for a Grand Slam win in tennis and Andy has done it in huge style.

"It's immense physical and mental endurance to win a game like that. I'm a keen tennis player myself. I can hardly last five games, let alone five sets.

"You're all on your own in singles tennis. There's no-one to blame but yourself when it goes wrong.

"He should have all our praise for such a magnificent game. The forecast of course was made yesterday that the great summer of British sport was over but he's given us another immense prize to wake up to."

Scottish First Minister Alex Salmond said the 25-year-old was now a "legend" in his homeland.

"Congratulations to Andy Murray on what was a fantastic performance," he said in a statement.

"This is another brilliant win over Novak Djokovic and continues an amazing year for Andy. Now Olympic and US Open champion, Andy truly is a Scottish sporting legend and I'm certain that more grand slam titles will follow."

Stirling Council, which presides over Murray's central Scotland hometown Dunblane, said it was looking to give the tennis star a homecoming fit for a hero.

"He's proved himself as an outstanding athlete and a man of true grit, and we'd love to offer him the freedom of the City of Stirling as a lasting mark of our thanks, our support and our respect," Stirling's Provost Mike Robbins said.

Roger Draper, chief executive of the Lawn Tennis Association, the sport's governing body in Britain, told BBC radio that Murray had pulled off "a phenomenal achievement".

"He's done it in an era where you've got not just Roger Federer -- the greatest player that's probably ever lived -- but you've got Rafa Nadal, Novak Djokovic as well."

Former British number one Roger Taylor, 70, a four-time Grand Slam semi-finalist, said: "Andy is on top of the world, very few people can beat him.

"I am sure he will go on to win many grand slam titles and become number one in the world," he told Sky Sports television.

"Finally British tennis is back on the map."