“I’m enjoying the role across all formats and I’d love to carry that on,” added McCullum.

“It’s been an absolute privilege to be in this position over the past three and a half years. I feel like we’ve made some significant improvements across the various formats.

“Yes, we’ve missed some opportunities, but I think this team has a real opportunity over the coming years to continue to improve and hopefully finish what we started. I’d love to be a part of that.”

Key backed McCullum during the Ashes, but neither ECB chief executive Richard Gould nor chair Richard Thompson have publicly spoken on his future.

At the end of the Ashes, McCullum also received support from Test skipper Ben Stokes, while the relationship between McCullum and Brook has blossomed during the T20 World Cup.

Asked after the semi-final defeat if McCullum should stay in charge, Brook said: “125%. I’ve said plenty of times he’s the best coach I’ve ever had.

“The way he speaks to everybody, he’s got an aura in the dressing room, and everybody looks up to him. The things he’s done over the four years since he took over has changed English cricket for hopefully the best.

“Our partnership has been good throughout the competition and since I’ve taken over. Long may it continue.”

Failures in away Ashes tours have often signalled change in the management of England teams.

Speaking on Sky Sports, former England captain Nasser Hussain said the ECB has to guard against repeating the mistakes of the past, while not ignoring the failures of this latest defeat in Australia.

“What you have to get away from is going to the Ashes, you lose, you get rid of the coach and captain, and you start all over again. I’m never a fan of that,” said Hussain.

“But I’m also not keen on, a couple of months later, forgetting what happened in the Ashes, and how poor England were on and off the field – all the mistakes that were made.

“There is a feeling Brook and McCullum are aligned, but there is a suggestion there was a divergence during the Ashes and that is a concern.

“They’ve made good decisions in the white-ball game that they didn’t in the Ashes. They missed an opportunity there and you can’t just brush over that.”