England’s international summer finished with a 5-0 series victory and a record 13th win after they beat New Zealand by 20 runs at Lord’s on Wednesday, but not before another spin-induced top-order wobble. Although Jon Lewis denied this was cause for concern before October’s T20 World Cup on spinning pitches in Bangladesh.

“I feel like we’ve got pretty much all bases covered at the moment,” the head coach said. “We’ve played some fantastic cricket over this series, and we’re confident that we can win the World Cup.”

With Lewis having already said that he will be sending an unofficial “A” side to Ireland in September, this was England’s last scheduled international before that tournament, but it was not quite the ruthless performance the captain, Heather Knight, had called for in her pre-game press conference. England were reduced to 83 for six – all six falling to spin – and relied on a battling innings of 46 from Knight and another weak showing by New Zealand with the bat to bail them out of trouble.

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A better side might well have overhauled England’s 155, but this was a thoroughly demoralised New Zealand, unfortunately habituated to losing. “We know that there’s bigger challenges ahead,” Lewis added.

Suzie Bates had been adjudged not out by the third umpire Anna Harris in the third over of the chase, who concluded Lauren Bell’s foot had not made contact with the ball before hitting the stumps after England appealed for a run out at the non-striker’s end. But three balls later Bell had Georgia Plimmer caught behind trying to scoop, while Bates lasted just three more overs before swiping Freya Kemp to mid-on.

There was no dramatic collapse from the tourists this time around – they were only three wickets down going into the death overs, with Amelia Kerr and Brooke Halliday putting on a 40-run partnership for the fourth – but a slow start meant they struggled to match England’s scoring rate. With 51 needed from 27 balls, Halliday reached for one outside off stump that should have been a wide, edged behind, and walked, knowing she – and her team – were beaten.

If anyone thought England’s problems against spin had gone away, the first 45 minutes of play proved otherwise. The left-armer Fran Jonas finished with career-best figures of four for 22, including the remarkable achievement of taking a wicket with the first ball of three of her four overs. Danni Wyatt pulled her to deep midwicket and Maia Bouchier sent up a soft catch to mid-on out of nowhere, but the third and fourth were ones to treasure – a caught-and-bowled effort diving to her right to remove Nat Sciver-Brunt, before a deceptive slider broke through the defences of left-hander Kemp.

At the other end, the off-spinner Eden Carson joined the party with wickets in consecutive overs: Alice Capsey hared down the track and was stumped, while Amy Jones failed to clear the very short long-on boundary and was caught on the rope. But Charlie Dean joined Knight to help England add 46 runs from the last five in a successful rescue operation.