Graham Thorpe, England's lead batting coach, admitted it is proving harder than ever to produce Test-quality batsmen.

Thorpe, who made 16 centuries in a 100-Test career, believes the increased onus on limited-overs cricket and the scheduling of the County Championship may have contributed to the difficulties in producing players who are accustomed to batting for a long time in varying conditions.

And while England built a 128-run lead on the second day at Headingley, Thorpe confessed to "a little edge of frustration" that every batsman in the top seven reached 20 but none have, as yet, gone on to register a half-century. Jos Buttler will resume on Sunday unbeaten on 34.

"Yes, without a shadow of a doubt [it is harder to produce Test-quality batsmen]," Thorpe said. "It is a challenge. It is tough [on early season pitches]. It's that ability to have a game that can work in different conditions.

"And there's the mental side of it. I don't know if the white-ball game has altered that to an extent, but that ability to apply themselves...Test cricket is longer and more mentally wearing than the one-day game. There's more thinking time and they have to understand they have to adapt and adjust to different conditions."

Thorpe's words largely echo those of England's head coach, Trevor Bayliss. After the first Test defeat, he questioned the value of playing on early-season Championship cricket where seam bowlers are sometimes provided copious levels of assistance. As a result, few batsmen play the long innings that tend to define Test matches. As a result, there is not the competition for places that the England selectors - and coaches - may desire and Wasim Khan, the Leicestershire CEO, is leading a working party looking into a better structure for the domestic game.

"We want to create competition for places," Thorpe said. "As teams often play better when they have that competition. At present, the one-day side has more players available than the Test side."

Perhaps the most impressive batsman on the second day was 20-year-old Dom Bess. Sent in as nightwatchman towards the end of day one, Bess failed by only one run to record a second successive Test half-century. And, so assured did he look, that at one stage Pakistan were bowling with two slips to him and three to Dawid Malan, while at another stage, the crowd mistook him for Joe Root - they chanted "Rooooot" - when Bess produced a perfect back foot force through the covers.

"He's shown some good character and fight," Thorpe said. "And he's enjoying the nightwatchman role.

"Eighteen months ago his batting wasn't at this level, so it shows the work he has put in. And, credit to the senior guys in the team, he has come into the dressing room and felt settled. I could say the same for Sam Curran and Keaton Jennings, too. They're all settled and natural in the dressing room."

Thorpe also admitted there had been some reflection among the batsmen after the first Test and felt there had been more application in Leeds as a result.

"After the first Test, which was a huge disappointment, the players have talked and probably had some hard words with themselves," he said. "But they've applied themselves here.

"There is a little edge of frustration that all the batters have got past 20 but none have got 50, but we're pleased with the lead. The game isn't in the bag, but we have shown some fight, character and application over the past couple of days and that has been pleasing."