Amir, Butt and Asif say they are innocent of the spot fixing claims
The three Pakistan cricketers questioned by police over alleged spot fixing arrived home on Saturday.
Salman Butt, Mohammad Asif and Mohammad Amir will return to England when required to do so by the police.
The trio, who maintain their innocence, flew from London to Lahore, before being taken out through an airport back exit to avoid media and protesters.
The players are accused of accepting money to deliberately bowl no-balls during the Lord's Test with England.
They have been provisionally suspended and charged by the International Cricket Council (ICC) and were interviewed under caution by the Metropolitan Police last week.
However, Pakistani interior minister Rehman Malik said they were allowed home for the Muslim holiday Eid after requests from their parents and the Pakistan Cricket Board.
A fourth player, left-arm paceman Wahab Riaz, will be questioned by police on Tuesday in relation to allegations of corruption.
Speaking on Friday, PCB chairman Ijaz Butt issued a statement explaining the players' return.
Pakistan confirm trio to return home
"They have not been charged by the police with any offence," said Butt.
"They have fully co-operated with the police in their enquiries and maintain that they are innocent of any alleged wrongdoing.
"They have agreed with the police to return to England if the police request them to do so to further assist the police in their enquiries."
Scotland Yard confirmed it was aware the players were returning home.
A statement said the trio "have given an undertaking through their solicitor to return to assist the Metropolitan Police Service inquiry in due course".
Pakistan's five-match one-day international series against England began with the
hosts winning by 24 runs on Friday,
with the second match at Headingley on Sunday.
Meanwhile, Pakistan also issued a statement through their solicitors denying reports that left-arm paceman Asif, 18, is planning to seek asylum in the UK.