A joint statement issued by the International Cricket Council (ICC), the England and Wales Cricket Board (ECB) and the Pakistan Cricket Board (PCB) said that no player nor team officials had “been arrested in relation to this incident”.
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It added: “As this is now subject to a police investigation neither ICC, ECB, PCB nor the ground authority, the MCC, will make any further comment.”
The statement said the ICC, ECB, PCB, along with the ICC Anti-Corruption and Security Unit, were assisting the police with their inquiries.
The BBC’s Andy Swiss said the allegations involved “very minor, very small details within the match that might seem ridiculously trivial to a lot of people”.
Our correspondent added: “That sort of information is worth a huge amount of money in the betting world where you can put bets on the tiniest details within a cricket game.
“This is a difficult situation for cricket and there are going to be some uncomfortable questions for the Pakistan team.”
Betting on when no-balls happen in cricket, or how many are made, is a form of gambling called spot-betting.
This refers to betting on certain events taking place in a game, rather than the actual result.
After taking 14 Pakistan wickets on Saturday, England took the final six wickets on Sunday morning to win the match by an innings and 225 runs.
This gave them a 3-1 victory in the four-match series of Tests, which are international matches played over up to five days.
England captain Andrew Strauss said the spot-fixing allegations against members of the Pakistan team had taken the gloss off England’s series win.
“I don’t think anyone wants to finish a Test series in this scenario,” he told BBC Radio Five Live.
“It has taken the gloss off the series win which is very disappointing because we had some outstanding performances.”
It is the second successive England-Pakistan Test series that has ended in controversy.
Four years ago, umpires Darrell Hair and Billy Doctrove ruled Pakistan had forfeited the fourth Test by failing to return to the field in time following the tea interval. The Pakistan team had been incensed about an earlier decision to penalise them five runs for alleged ball-tampering.
In July 2008, the ICC changed the result of the match from an England win by forfeit to a draw, but in February last year cricket’s governing body made a U-turn and awarded a victory to England.
It is also the second time this year that the Pakistan team has found itself under investigation.
An inquiry was launched after they lost every international fixture on last winter’s tour to Australia, resulting in four players being suspended by the PCB and three players fined.
Three of the bans were subsequently lifted, including indefinite bans on former captains Mohammad Yousuf and Younis Khan, and the fourth is currently subject to an appeal.
Pakistan quartet under the microscope over allegations
Still only 18, during day two of the second Test at Lord’s the left-arm paceman became the youngest bowler in Test history to take 50 wickets.
He went on to take his best Test figures, picking up 6-84 in England’s only innings, and is currently ranked the eighth-best bowler in Test cricket.
He made both his Test and one-day debuts in July 2009 and has gone on to snare 51 Test wickets at a shade over 29 runs apiece, and has a further 25 victims in one-day internationals.
Born in Gujjar Khan, Punjab, he has a whippy action that enables him to swing the ball both ways at a lively pace that can touch 90mph.
Of the three no-balls bowled which led to the investigation, Amir is alleged to have bowled two of them, one on Thursday and one on Friday.
A controversial figure who has twice been suspended after testing positive for banned substances – although one ban was subsequently overturned – and who was also detained in Dubai for suspected possession of illegal drugs.
He is a fine swing bowler who can manipulate the ball sufficiently at no more than medium pace – he says “pace is nothing” – to remove the very best at Test level.
Although he could bowl quicker he is happy to hover about the 80mph mark and his guile and ability to move the ball both ways have brought him 106 Test wickets at an average of 24.36.
Now 27 he made his Test debut in 2005 and is currently ranked third in the ICC bowling rankings.
He is alleged to have bowled one of the three no-balls in question on Thursday, the first day of the Test at Lord’s.
The 25-year-old was only appointed Pakistan’s Test captain in July after Shahid Afridi stepped down from the role – after a single game in charge – following their defeat in the first game of their two-Test series against Australia earlier this year.
Butt had previously been appointed vice-captain at the beginning of the tour after a number of senior players were discarded following what turned out to be a disastrous trip down under.
A stylish if inconsistent left-hander, who averages 30.43 from 30 Tests, he has proved more successful in ODIs, scoring 2,725 runs at an average of 36.82, including eight centuries.
He made his debut back in 2003 but was in and out of the side for several years until nailing down a regular place in 2007.
Along with Amir and Asif, Butt has had his telephone taken away by police but he said: “These are just allegations and anybody can stand out and say anything about you, it doesn’t make them true.”
The wicketkeeper was interviewed by the police along with the other three on Saturday night.
Kamran, older brother of batsman Umar, is renowned more for the explosive nature of his batting than the quality of his glovework.
At 28 he has already played 53 Tests and 118 ODIs, adding 184 Test catches and 22 stumpings to his 2,648 runs at 30.79 in the longest form of the game.
He was fined and put on probation by the Pakistan authorities after their dire tour of Australia in 2009-10 and a poor all-round display in the first Test against England led to him being dropped, only for the broken finger suffered by his replacement, Zulqarnain Haider, to see him recalled for the third Test.
He made his debut back in 2002, with the biggest of his six Test centuries the unbeaten 158 he scored against Sri Lanka in 2009.