As the tampering saga begins to recede – or is this just a little lull? – it is no longer possible to hide the fact that England’s Test team is undergoing a good old-fashioned crisis, stemming from a lack of runs, rather than integrity, among their batsmen.

Fortunately for Joe Root his all-rounders came good in the final session at the Hagley Oval to keep England afloat. In this case it was Jonny Bairstow, who steered England to a total approaching respectability with an excellent, unbeaten 97. His chief ally was Mark Wood, who we can elevate to all-rounder status for a while, after he hit a vibrant 52, his best score in Test cricket. We know about Bairstow’s refined belligerence down the order but there were times in their partnership when the quality of Wood’s strokeplay made it hard to distinguish them.

This pair added 95 together in 18 overs, an alliance that papered over another alarming batting performance. It may be that some of the batsmen are mentally numb, others may be rusty, but on a sublime day for cricket it became all too evident that England possess only three batsmen in their top seven capable of suggesting any kind of permanence at the moment, even on a perfectly benign surface.

Beyond Root, Ben Stokes and Bairstow there is currently a quartet who seem as fragile and fleeting as a rainbow but not so pleasing on the eye – with the possible exception of James Vince when cover driving. Sadly that quartet now includes Alastair Cook, who was defeated by Trent Boult once again.

The autumnal sun beamed down from a cloudless sky. The locals claimed their spots on grassy banks still damp with dew when Kane Williamson won the toss. Following the pattern of the four previous Tests here he opted to bowl despite the overhead conditions. England had made three changes from Auckland, with Vince, Wood and Jack Leach, who was making his debut, replacing Moeen Ali, Chris Woakes and Craig Overton. By recent England standards this constituted a radical overhaul.

Up stepped Boult and in his third over he clean bowled Cook. It was a fine, full delivery that deviated from leg to off and, with Cook’s feet stuck on the crease and his bat lunging desperately in front of him, he missed the ball by a remarkable distance given he has more than 12,000 Test runs to his name.

Cook’s dismissal did not preface an Auckland-style subsidence, although there was some swing and nip for the pace attack. Mark Stoneman, off the mark after an inside edge sped perilously close to his off stump, played and missed frequently while Vince looked more assured. As ever a couple of drives purred from the middle of his bat as the Kiwis kept searching for swing via a full length. Then, on 18, Vince was stuck on the crease against Tim Southee and was lbw, with the replays confirming that the ball would have clipped leg stump. Like so many of the batsmen he needs a substantial score in the second innings to guarantee his place in the next Test team.

Root settled easily and scored without difficulty, often on his toes and punching the ball through the offside. He navigated the side to 70 for two at lunch, not a bad foundation after being put into bat. For another half an hour after the interval all was serenity. New Zealand tried a review against Root that reflected how dangerous the England captain was looking.

Root drove Southee to the onside boundary to confirm this but then he tried to clip another full-length delivery through midwicket and was bowled. Without looking back at the damage he marched off swiftly, disgusted with himself.

From here there was mayhem. Dawid Malan missed his first ball from Boult and set off for the pavilion before the umpire’s finger was properly raised. It was as if he had never sighted the ball. In the next over Stoneman’s luck ran out as he edged a handy delivery from Southee into the safe hands of Tom Latham at second slip.

Stokes and Bairstow, batting properly, now added 57 but after tea Stokes was caught down the leg side off Boult. The standard response to this dismissal is to say that he was “strangled” but this happens so often now, especially against left-handed bowlers, that the batsmen must take note of an error rather than bemoan their bad luck. Stuart Broad, elevated to No 8, did not bat like one, soon chipping an easy catch to mid-off against Southee. But Wood did.

There were several crunching cover drives and as well as a six hooked off Neil Wagner. Wood had not played against a red ball since September. Practice? Who needs it? Having posted his maiden half-century in Test cricket he was bowled by Southee. All the while Bairstow had mixed discretion and aggression adeptly as he often can with the tail. The crack of two pull shots against Wagner echoed satisfyingly around the ground.

After Wood’s departure, Leach supported Bairstow with impressive composure throughout the final 10 overs. For the New Zealanders the old firm of Boult and Southee did all the damage, with the latter the more potent this time, but thanks to Bairstow and the infusion of new blood – perhaps England should try this more often – the Kiwis were still in the field at the close.