Peter Moores has conceded that England will have to sharpen up their act in Friday’s second Test against Sri Lanka at Headingley and beyond now that Alastair Cook is under threat of suspension unless their over rate improves.

Cook was fined 20% of his match fee because of England’s slow over rate in the first Test at Lord’s, and the other 10 players 10% of theirs, by Andy Pycroft, the former Zimbabwe player who is the International Cricket Council’s referee for the two-match series.

Pycroft ruled that England had been a single over down on the minimum number they should have bowled at Lord’s, which on the face of it seems lenient as they bowled only 84 of the stipulated allocation of 90 in a full day in the field on Saturday. That will not worry any of them too much, with the agonising near-miss on Monday evening leaving a far more bitter aftertaste. But the ICC regulations, under which a captain will be suspended if his team commits a second offence in the space of 12 months in the same form of the game, does leave Cook under pressure.

India’s captain, MS Dhoni, missed a Test in Australia in 2012 after being found guilty of a repeat offence; Sri Lanka’s Angelo Mathews had to sit out two one-day internationals last year; and during this year’s World Twenty20 both Sri Lanka’s Dinesh Chandimal and South Africa’s Faf du Plessis served a one-match ban.

Cook conceded it was an issue for England largely because of the new balance of their team, with four specialist seamers – who bowled 194 of the 229 overs they delivered at Lord’s. In this area, as in so many others, England’s captain and coach are left to rue the retirement of Graeme Swann.

“We have already started to address that during the game,” said Moores, who was predictably enthused after such a memorable return to Test cricket. “We have already quickened up … we don’t want to lose overs at all because it can be costly and it’s something to be aware of.”

However, he suggested it would be simplistic to conclude that the slow over rate earlier in the match had cost England crucial overs at Sri Lanka’s last pair on Monday evening. “I don’t think it had as much bearing as maybe it looked,” Moores added. “The pressure at the end of the Test helped to create some of the chances we got because the pressure on the Sri Lanka batsmen made them make a few mistakes.”

He did not deny, however, that the lack of any obvious successor to Swann as a specialist spinner is a major concern – and not only because of its effect on England’s over rate. “We are going to have to identify our next spinner, there’s no doubt about that,” Moores conceded. “All sides need the option of a frontline spinner to be able to play in all conditions. Otherwise it is going to be a weakness in our ranks that people will be able to try to exploit.”

Monty Panesar and Scott Borthwick each played a Test in Australia following Swann’s retirement immediately after the Ashes were lost in Perth. But Borthwick has hardly bowled so far this season for Durham, and Panesar’s form for Essex has been no better than steady, with more notice taken of a couple of disciplinary breaches, albeit minor.

Simon Kerrigan, who worked closely with Moores at Lancashire, is still fairly early in the process of rebuilding his confidence after the mauling he endured from Shane Watson on a shock Test debut at The Oval last August, and the cupboard is so bare that the former England captain Andrew Strauss has called for Adam Riley, a 22-year-old in his first season as Kent’s first-choice off-spinner in place of James Tredwell, to be fast-tracked into the squad for the second series of the summer against India.

“The names are out there,” said Moores. “Kerrigan, obviously Riley has come on the scene, and Monty is the most experienced Test match bowler out there but through other issues has made it very difficult to look at him at the moment as an option. Where that goes to in time we will just have to wait and see.”

But, for the moment, Moores is happy to stick with Moeen Ali, who bowled 28 overs on his Test debut and claimed Kumar Sangakkara as a notable first scalp. “I think he has the chance at the moment,” said the restored coach. “What was really nice was the way he handled himself in the Test match. He didn’t bowl a lot and he showed as a bowler he is getting better quite quickly. When we saw him in practice it’s more than an occasional spinner bowling, he gets decent revs on the ball, dip and drift. “He is going to have to adjust to bowling in Test cricket if he is going to take wickets as a Test match bowler but he has that opportunity. At the moment we are playing him as much as a batter as well because as we saw in this Test match he looked very comfortable out there, hit his first ball over the top and had the confidence to play well.”

At least the wicketkeeping issue that had also exercised England in the buildup to Lord’s would seem to have been settled, with Moores confirming that Matt Prior had come through a stiff test for his achilles with no reaction. “We had no issues – Matt is 100%,” said Moores. “That pitch was difficult and I thought he kept beautifully.”