England's performance with the bat on the opening day of the second Test against Pakistan was a huge improvement on their dismal showing at Lord's.

Beaten by 75 runs amid a flurry of rash strokes in the first match of the series, they were heavily criticised by fans and media.

In reaching 314-4 at Old Trafford, England proved they had looked at what happened, talked about it and worked things out.

Captain Alastair Cook, with a typically composed 105, and Joe Root, who made an even more assured unbeaten 141, were at the forefront of an impressive response.

If there was a recklessness at Lord's that stemmed from a desire among the England batsmen to impose themselves on the bowlers, here they played proper Test cricket.

Cook and Root were magnificent, compiling patient, well-paced innings that every other batsman - on both sides - would be advised to follow.

Learning the lessons of Lord's

We must remember that Pakistan's is a very unusual attack - how often do you see three left-arm seamers and a leg-spinner in a side? - and Root adopted the unusual tactic of taking an off-stump guard to combat them.

John Holder, who spent 27 years as a first-class umpire, said he had never seen a player bat on off stump during his career.

It certainly worked for Root. It helped him decide what to play at and what to leave - I can only remember the ball beating his bat a couple of times all day - and he played much straighter than he did at Lord's, when he was caught slog-sweeping and on the pull.

Conditions undoubtedly helped England, who, by winning the toss for the first time in five Tests against Pakistan, enjoyed first use of a typically true Old Trafford surface under clear skies.

I wrote earlier this week that England needed to learn how to play leg-spinner Yasir Shah. They did that with aplomb.

Pakistan's match-winner at Lord's with 10 wickets, Yasir barely spun a ball all a day. He ended it with figures of 0-111.

For that, Root and Cook can take the bulk of the credit. They made Yasir work for his wickets - no swipes across the line, no charges down the pitch. Crucially, there were no easy pickings.

Vince's chances running out

As impressive as Cook and Root were, there are still concerns over the rest of the England top five.

Alex Hales made only 10, but equally worrying was the manner in which he was worked over by Mohammad Amir - bowling full, swinging it away and then bringing one back in to bowl the opener comprehensively.

After such a good series against Sri Lanka - he made three scores in excess of 80, and averaged 58 - it feels like we are back to where we were with Hales during the winter tour of South Africa, when people were questioning his technique against high-quality opening bowlers.

Gary Ballance will rue his dismissal for 23 late in the day, while James Vince missed another chance to press his case with a modest 18.

Caught in the slip cordon at Lord's, he was dropped at second slip on the drive today before finally edging another loose drive off Rahat Ali.

Test cricket is a test of patience - it is the batsman against the bowler and a matter of who will crack first. Vince cracked.

He has not convinced me yet as a Test cricketer, and if he does not get runs in the second innings I am not sure he will keep his place for the rest of the four-Test series.

England's missed opportunity

England played superbly on the first day and may well go on to win this game but, regardless of the result, they missed a golden opportunity to play two spinners at Old Trafford.

Leg-spinner Adil Rashid should have been picked to complement Moeen Ali's off-spin.

On a pitch that traditionally favours the slower bowlers, in dry conditions and with tours of Bangladesh and India looming this winter, England should have had another look at Rashid and left out Vince.

They have so much batting depth and so many all-round options they could afford to play one less specialist batsman. Who knows, Rashid may well have scored more runs than Vince anyway.

As it is, Rashid's only chance may come in the final Test at The Oval, which gives him a solitary game to get accustomed to Test cricket again before England's tour - plus the added pressure of having to impress.

Starting from zero

Given what happened at Lord's, England's ideal scenario at Old Trafford would be to win the toss, post a big score and Yasir to have 0-100 by the end of the day.

In that respect, they could not have asked for much more on Friday.

But the familiar failings of Hales, Vince and Ballance are no closer to being rectified.

Although England remain well placed to post an imposing total in excess of 450, all the batsmen, including Root, must start from zero on Saturday.

So there is work to be done, not least with Root and Cook's top-order colleagues.

Jonathan Agnew was speaking to BBC Sport's Justin Goulding.