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England completed a 2-0 series whitewash with a commanding 247-run victory over New Zealand in the second Test at Headingley on Tuesday.
This was England's last test before the Ashes opener at Nottingham's Trent Bridge ground in July.
Australian batsmen have struggled against the swinging ball in recent Ashes series and McCullum said: "England are red hot favourites at home, their ability to swing the Duke ball is huge. Any team that plays at home is familiar with the surroundings."
McCullum added the defining moment of his team's test campaign against England had been the fourth day of the first Test at Lord's.
New Zealand collapsed to 68 all out, England paceman Stuart Broad taking a Test-best seven for 44, as they suffered a 170-run defeat.
"Right up until that point our self-belief was very high and that ripped our hearts out and just started to create some self-doubt among us which is a horrible thing in this game," McCullum said.
Headingley saw New Zealand experience fresh batting woes, mainly against offspinner Graeme Swann who took 10 wickets in the match.
"That's what unfolded in this Test," McCullum added after the tourists could only manage 174 in reply to England's first innings 354 before being bowled out for 220 in pursuit of an improbable 468 for victory.
What made the result all the more galling was that in New Zealand earlier this year the Black Caps held England to a 0-0 draw in a three-test series and were just one wicket away from claiming victory in the Auckland finale in March.
"Yeah, definitely a step backwards," said McCullum, whose seamers posed problems for England.
"It's incredibly disappointing but if you look back on the last five Test matches we've played some good cricket and taken some strides forward but it's fair to say this one was a step back."
New Zealand don't play Test cricket again until they travel to Bangladesh in October.
"It is a big gap for the test side and we'd love to play more Test cricket but we've got to earn the right," McCullum said.
However, McCullum hoped the arrival of some seasoned players for a three-match one-day series with England, starting at Lord's on Friday, and the subsequent Champions Trophy, would reinvigorate the side.
"We've got eight new guys coming into the fold for the ODI series and Champions Trophy and they're quite experienced, some of those guys.
"One thing we have been able to do in recent times is move between the forms of the game and refocus too. That's what this (situation) is going to require on a very short turnaround."
McCullum, who gave up wicket-keeping in Tests because of back and knee problems, found himself behind the stumps after BJ Watling suffered a knee injury at Lord's and donned the gloves again at Headingley.
But the arrival of Luke Ronchi for the one-day series could free McCullum up to play as a batsman only.
"It's something we need to talk about in the next 24 hours before we start to nail down that one-day team but it's definitely up for discussion.
"He (Ronchi) is definitely going to play as an opener."
New Zealand's chances at Headingley were not helped by left-arm quick Trent Boult being off the field for most of England's second innings after he aggravated a side injury.
In Boult's absence, England captain and opening batsman Alastair Cook scored 130.
"He's not looking great, he has a scan in London, he's still not moving that freely which is a shame because he's been a revelation for us this season," McCullum said of Boult.
"When we play England with Alastair at the top, it's going to be harder to get a dismissal."
