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Pace bowler Ollie Robinson is unlikely to play for England until the Test series against South Africa in August because of an ongoing back issue.
The 28-year-old has had a scan, which proved inconclusive, and an injection, meaning he is likely to have at least three more weeks out.
He will miss the rest of the series against New Zealand and the rescheduled fifth Test with India in July.
The three-Test series against South Africa begins on 17 August.
Robinson has not played for England since the fifth Ashes Test in Australia in January.
He travelled to the West Indies for the series in March, but missed all three Tests, then was not selected for the first Test against New Zealand after a number of fitness issues restricted his bowling for Sussex in the early part of the summer.
The right-armer was due to play for a County XI against New Zealand, but pulled out on the morning of the match because of stiffness in his back.
Meanwhile, left-arm spinner Jack Leach took part in England training on Wednesday before the second Test against New Zealand, which begins on Friday.
Leach was withdrawn on the first day of the first Test with a concussion following a heavy tumble in the field. He was replaced by leg-spinner Matt Parkinson, who made his Test debut.
England won the first Test by five wickets, ending a run which had seen them win only one of their previous 17 matches.
It also gave victory to captain Ben Stokes and coach Brendon McCullum in their first Test in charge.
"We're obviously super positive," opener Alex Lees told BBC Sport.
"The result was what we wanted, but the more pleasing thing was the manner in which we did it."
The Lord's Test was Lees' first on home soil and his first taste of victory in four attempts.
The left-hander has yet to pass 31 in Test cricket, but skipper Stokes said the 20 he made in the second innings was Lees' best knock in an England shirt.
"He's probably right," added Lees. "I want to make a big contribution and I'm confident that if I play like that consistently, I should be alright.
"I said to Baz [McCullum], tongue in cheek, 'The openers are like the Volvos, then you've got the supercars coming in in the middle order'. We might get through an hour or an hour and half and only get a 20 or 30, but sometimes that is invaluable."
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