The Kiwi captain rejects the suggestion that England showed their hosts any lack of respect in the 0-0 stalemate over three Tests in New Zealand two months ago, reasoning instead that his team simply grasped the initiative there from the outset. He anticipates, however, that Alastair Cook's men will be even tougher nuts to crack at home.
"They will be more aware of us. They're playing in their backyard as well, so we know we're going to have to improve on the performance at home," McCullum said.
"They will probably swing the ball a bit more than in New Zealand, where they also struggled a touch with the Kookaburra (ball).
"They will be a far more dangerous proposition. Their batters are very clinical at home, from what we've seen. We believe we have some guys favoured by these conditions, but we'll have to be on our game. It's pretty mouth-watering."
Cook and Co have had to respond to accusations of complacency after failing to consolidate their historic success in India before Christmas with more in New Zealand afterwards.
But McCullum said: "I don't think England were disrespectful. We started the series really well and were able to get into it with a dominant display, which allowed us to grow in confidence and ate away at theirs too. If you look at the rankings, we punched above our weight. But that's the standard we have to operate at."
McCullum, open in public about his pre-match plans in direct contrast to England's preference for playing their cards close to their chest, confirmed the tourists are considering an all-pace attack at Lord's. It will therefore be a direct choice between naming Doug Bracewell as fourth seamer, or Bruce Martin as a frontline spinner.
Either way, McCullum is well aware he is unlikely to have the freedom to dictate the pace throughout two back-to-back Tests against opponents ranked six places above his team. That was the case in New Zealand, apart from in the rain-ruined middle match in Wellington, but McCullum acknowledges it cannot always be so.
"For the majority of that series, we were either on par or with our noses in front," he said. "The next challenge is to captain when we're behind the game, to get us back in the contest."