Jack Draper and Andy Murray are both tennis players, but that’s just about where the likeness stops. At 22, Murray was still feeling his way into the spotlight after reaching the quarter-finals of Wimbledon, painted at the time as some kind of misanthrope, an implacable grump. By contrast Draper, who plays in his first grand slam quarter-final on Wednesday, is embracing the fame. “I quite enjoy being in front of the camera,” he told British Vogue while doing a cover shoot this summer. “If I’m looking good, that is.”

Draper posed in checked coats and leather jackets with curls of hair bouncing off his forehead like Danny Zuko, one of his many hairstyles. “I’ve done a buzzcut, a mohawk, a mullet…” he said. Meanwhile, Murray was recently asked what advice he’d give to his younger self. “Get a haircut,” he replied. “And get some clothes that fit.”

And yet for all their differences, there is an obvious and irresistable link. Murray’s third piece of advice to himself was to enjoy tennis before it’s gone. Now it is gone, and as Draper became the first British man to reach the last eight of a slam since Murray in 2017, there was an unmistakable sense of the torch being passed.

Draper thrashed the very capable Tomas Machac in the fourth round of the US Open and said he was immensely proud to be following in the footsteps of his friend and an “icon of the game” in Murray. “I miss him in the changing rooms. I miss being next to his stinky shoes and all of his stinky clothes. Andy is a legend. If I have half the career that he’s had then I’ll be a happy man.”

Draper’s rise was somewhat different to Murray, who grew up in Dunblane and moved to Barcelona as a teenager. Draper is the son of the former Lawn Tennis Association chief executive Roger Draper and Nicky Draper, a British junior champion. He attended the private Reed’s School in Surrey and was coached from a young age, developing a powerful left-handed serve and forehand despite being naturally right-handed.

By this point in his career, Murray had reached multiple slam quarter-finals, had won four ATP titles and was ranked No 4 in the world. Draper is No 25, with one tour title so far, the Stuttgart Open he won in June. That difference is partly a gap in natural ability, but it is also explained by Draper’s struggles with a plethora of injuries – back, hip, ankle, shoulder – which have meant that this is really his first year of sustained play.

“My body was made of glass,” Draper recently said of his struggles in 2022 and 2023 – and here there is a parallel to Murray, whose body broke down as a young emerging player, which drew some criticism in the media. Murray went away and worked on his physique in the winter of 2007/08, and came back the following season unrecognisably stacked, leading to his famous bicep-flex celebration at Wimbledon the next summer.

Draper has worked hard in the gym over the past 12 months to become more physically resilient. He admits he has not always adopted a professional mindset, indulging in fast food and enjoying a night out and a few beers, as a comic video of a boozy car ride home with Murray last year suggested (Murray stoically drives as Draper sings I’m Gonna Be 500 Miles at the top of his voice while swigging lager).

In New York this week, Draper has returned straight to his hotel after matches or practice, ordering healthy food via Deliveroo and watching a movie. His coach has banned coffee with caffeine.

“I can make a cup of tea in the room and then watch a series or something,” he said of his new puritanical lifestyle. “I watched Gangs of London recently. Just anything to conserve mental and physical energy, whether that’s calling home or just being chilled. It’s sometimes a bit of a lonely existence being a top tennis player. You have just got to make many sacrifices.”

He has reached a whole new level this summer, not just in his achievements on court but with the manner of them. His run here to the quarter-finals at Flushing Meadows has been immaculate, without a set dropped, and the way he blasted Machac off the court with peerless serving and a flurry of booming forehand winners felt like a statement to the rest of the field.

Up next is a stiffer test in Australia’s Alex de Minaur, the world No 10 whose girlfriend is Draper’s good friend, fellow British No 1 Katie Boulter. De Minaur won all three of their previous contests but they were close affairs, the most recent of which Draper forfeited with injury. The winner will have a serious chance of lifting the trophy in a tournament without the beaten Carlos Alcaraz and Novak Djokovic.

Even if it doesn’t happen this time, Draper has shown enough to suggest he can one day emulate Murray and become a grand slam champion. He will forge his own path and it would be unfair to expect a repeat of Murray’s achievements: reaching world No 1, winning three slams in 11 finals, claiming 46 titles in all including two Olympic golds and a Davis Cup won with a lob from the gods. British tennis may never see another Murray, but at least Draper won’t have to face Roger Federer, Rafael Nadal and Djokovic in their prime.

Whatever he achieves, Draper will have Murray’s support. The pair trained together while Murray recovered from hip resurfacing surgery in 2018, which gave the young Draper a chance not only to hit with one of the world’s best players but to pick his brains, a resource he still taps. “When I do have a question,” he said this week, “I will often pick up the phone and I will speak to Andy and get his advice on things.”

Perhaps one difference between the two at this stage of their careers is that the world seems to know Draper already, in a way they didn’t with Murray, at least at first. As well as being a self-confessed tennis nerd, he is a football fan (Manchester United), passionate about music (rap, grime and Oasis) and an animal lover (he lives with Ozzy the dog in south-west London). “If I’d have called him Rafa or something it would have been a bit cringey,” he explained.

It is a well-rounded life, but Draper has dedicated himself to his profession with new zeal in recent months and it is paying off. He is in the best place of his career, fit and in form, utterly focused on his goal of climbing the rankings. Although, there are still little signs of a colourful life beyond the court: as he dismissed Machac, Vogue editor Anna Wintour watched on from his box. Murray had a few more titles by this stage, but he never had that.