Brendon McCullum says his England side are about much more than aggressive cricket, labelling the term 'Bazball' "silly" as he responded to Steve Smith's comments about the team's revival.

England have looked reinvigorated since McCullum and Ben Stokes took over as red-ball coach and captain respectively.

They have posted three of their highest-ever run chases in their last three Tests after a remarkable victory over India at Edgbaston.

Having whitewashed world champions New Zealand 3-0, England completed a 378-run chase against India on Tuesday, drawing the teams' delayed series and sparking new levels of excitement among fans.

'Bazball' – the term coined to describe England's aggressive style under the New Zealander – has won near-universal praise, but the coach himself says it does not do justice to their displays.

"I don't really like that silly term that people are throwing out there," he told Australian radio station SEN. 

"Because there's actually quite a bit of thought that goes into how the guys manufacture their performances and when they put pressure on bowlers and which bowlers they put pressure on. 

"There's also times where they've absorbed pressure beautifully as well."

Former Australia skipper Steve Smith is among those yet to be convinced by England's style, recently declaring to the Sydney Morning Herald: "I'm just intrigued to see how long it lasts, if it's sustainable."

Australia's 4-0 Ashes humiliation of England in December and January irreversibly damaged Joe Root's captaincy, with the next edition of the teams' Test rivalry set for 2023.

McCullum insisted Smith was right to question England, adding Australia would provide the biggest challenge of his tenure but stressing his immediate focus was on the three-part series with South Africa, set to begin on August 17 at Lord's.

"I saw those [comments] flick up on one of the feeds somewhere," McCullum added. "It's quite right, it is going to be a big challenge when we take on Australia.

"It's going to challenge our method, and it's going to challenge what we're capable of achieving and that's pretty exciting I reckon.

"Isn't that what the game's all about? To sort of reinvigorate yourself and then be confronted against the very best.

"I do believe that both New Zealand and India are two very, very good cricket sides as well. Australia is a different kind of challenge because of the history of the Ashes and the rivalry which exists there.

"We know that's probably the ultimate challenge for us. We'll have to deal with that in time, I guess. In this job you plan as if you'll live forever and live as if you'll die tomorrow.

"You want to make sure you enjoy the ride. I keep preaching to the boys about being where your feet are and to try to immerse yourself in the here and now.

"You take your eye off anything, and teams will be able to make sure you look a bit silly. Our focus will be on South Africa for now but at some point in time, that will be a series which we [focus on].

"Test cricket needs the Ashes to be strong and competitive. You'd say the last one wasn't so that's the task for us in time."