Alastair Cook has said he feels “privileged” to be the latest England Test cricketer to be inducted into the International Cricket Council hall of fame. Cook becomes the 33rd England player to join the esteemed list of names including WG Grace, Shane Warne, Brian Lara, Ian Botham and Viv Richards.

The former England women’s captain Charlotte Edwards was the last England player to be inducted, in 2022, while Bob Willis – England’s 1981 Ashes hero at Headingley with the ball in hand – was given the honour posthumously in 2021 alongside the former Test captain and chairman of selectors, Ted Dexter.

The most recent Englishman to be given the accolade, from date of last Test match rather than date of induction, was Cook’s former mentor Graham Gooch. Speaking before the ICC announcement, Cook paid tribute to his fellow Essex and England opener: “Graham was a kind of mentor, friend, coach, you name it – he’s done everything for me. We never played in the same team, thankfully, as he was obviously a far better player than me!”

Cook and Gooch both rose to the top of the England men’s Test batting tree despite different playing styles. Long before Prince Andrew’s glandular revelations to Emily Maitlis, Cook was renowned for his “ability” to forgo sweating even in the most searing conditions.

In 2015 he batted for 836 minutes to score 263 runs off 528 balls against Pakistan in Abu Dhabi. In what was to become the third-longest Test innings on record, Cook barely even asked for a change of gloves and emerged fresher than an alpine snow drift whenever he removed his helmet to acknowledge the latest innings milestone. The left-hander was known for his obdurate defence and limpet-like occupation of the crease.

The right-handed, white-helmeted and ursine Gooch was earmarked as a heavy-batted big hitter in his early career and on his day could swashbuckle runs against the most potent Test attacks of the 1970s, 80s and 90s. His second-innings 154 not out against a lightning-quick West Indies bowling lineup in day-long Yorkshire gloam at Headingley in 1991 is cited often as a high watermark of English batting.

Both men have recently seen their batting records challenged and overtaken by England’s current Test outfit. Cook’s English Test records of 33 Test centuries and 12,472 runs were surpassed by Joe Root in his past few outings and in Multan last week Harry Brook became the first English player to hit a triple century since Gooch’s 333 against India at Lord’s in 1990. Brook fell for 317 to end up fifth on the list of all-time English highest scores, Gooch remaining in third place but surely not sitting comfortably for long with the way Stokes’s and McCullum’s players seem intent on toppling Test records like a toddler playing Jenga.

Cook said he rang Root last week when the Yorkshireman eclipsed him as England’s all-time leading Test run scorer. “I watched the moment and I rang him after the end of the play. I couldn’t think of the right words to write in a text message, so I thought: ‘I’ll just ring him, see what he was up to and to make sure he had a beer in his hand.’ I think he did.”

After going past Cook, Root now sits fifth on the all-time Test scorers list with only Rahul Dravid, Jacques Kallis, Ricky Ponting and Sachin Tendulkar ahead of him. Tendulkar’s 15,921 Test runs puts 3,257 runs of daylight between the Indian great’s total Test tally and, as it stands, Root’s 12,664. “You just never know,” Cook said on the likelihood of Root hauling in the little master. “I hope he can get very close, if not be the first person to score 16,000 Test runs, it’ll be a great achievement.

“I’ve never seen a team push the boundaries as much as this England team have done. There’s obviously been great sides in the past who would score quickly but not quite as quickly as this side seem able and willing to do.”

The former Test captain thinks the current England Test batting lineup have the attributes to do well in Australia during the Ashes series next winter. “The current top six have plenty of experience of Test match cricket now and in an ideal situation will be the batters going to Australia. Those players have certainly got potential to do well there … I think the flat wickets suit the batting lineup that England have.”

Reflecting on his own England career, Cook said he “left no stone unturned … every time I pulled on the England shirt, I tried my best to be as good as I could be.”

He may no longer be England’s No 1 but Cook could well be the last of his kind. He has his place in the history books and, now, the hall of fame. With no danger of being dismissed from either.