Graham Gooch hailed Alastair Cook as a "fantastic servant to England and cricket in general" after the opener reached the landmark of 10,000 Test runs on Monday.
By taking his score to five not out on day four of the second Test with Sri Lanka, as England pursued a modest victory target of 79, Cook became the first Englishman to amass 10,000 runs in the five-day format and replaced Sachin Tendulkar as the youngest player of any nationality to do so.
Former England skipper Gooch, who was last year surpassed by Cook as his country's leading Test run-scorer, lauded the left-hander's achievement.
"Anyone who interrupts my apple pie and custard on a Monday afternoon has got to do something special," joked Gooch on the BBC's Test Match Special.
"Alastair has been a fantastic servant to England and cricket in general, a great ambassador. To get 10,000 runs, to average 1,000 Test runs a year since his debut is a phenomenal achievement.
"He's been the rock of the England batting for a decade and I hope he goes on for a while."
Gooch has worked closely with Cook as a batting coach for much of the latter's career with Essex and England.
"He's a guy that gets the job done," Gooch added. "He's an old-fashioned sort of Test player now, in the modern era. A lot of the players around the world have been brought up with T20 and one-day cricket, they're of a different nature. Cook is a player who is very valuable in the Test team because he not only occupies the crease, he goes big if he gets in and he helps win matches.
"He's sort of a dying breed, but he's a very valuable asset to his team. It's not always about how many runs you score, it's how many matches you win for your team and he's been at the forefront of that for the last decade."
Asked whether Cook can go on to score many more Test runs, Gooch said: "I'd like to think so. He's got his farm in the background, he loves his farming, so he has had something else to occupy his mind over the years, which has been a great asset for him because he's been able to take his mind off the game.
"As long as the motivation, the desire, the will is there, I don't think the physical side will be a problem for him. It's just whether he wants it enough and I hope he does because he has been a great hero to a lot of English cricket supporters and he's given some exhibitions on how to score Test runs."