 The cause of Woolmer's death is not yet known |
Spokesman Pervez Mir said there was silence, not confrontation, in the wake of the team's surprise World Cup defeat by Ireland on 17 March.
Woolmer was found strangled in his hotel room early the next day.
Jamaica's deputy police commissioner said that CCTV from Woolmer's corridor has now been recovered.
Mark Shields said that the tapes came from security cameras installed on the 12th floor, where Woolmer's room was located.
Squad quizzed
Mr Shields said that the cameras were installed at either end of the corridor and that, while they did not show Woolmer's actual room, they should tell police who came in and out of the passageway.
"They are crucial as they may give us an image of the murderer or murderers of Bob Woolmer," he said. 
They are crucial as they may give us an image of the murderer or murderers of Bob Woolmer 
Mr Shields said that the footage would now be converted onto a digital format so that it can be properly examined and to ensure that the original film does not get damaged in any way.
Jamaican police investigating the murder questioned Pakistan's players before they left the island.
Pakistan captain Inzamam-ul-Haq, team manager Talat Ali and assistant coach Mushtaq Ahmed spoke to police on Saturday.
Mr Shields said the extra questioning had been only a formality.
The squad has now landed in Britain and hopes to leave for Pakistan on Sunday night, Mr Mir told the BBC.
Rift rumours
Speaking after the squad arrived at London's Heathrow airport, Mr Mir said the players were shell-shocked by the surprise loss to Ireland, which saw Pakistan eliminated from the World Cup.
There was no confrontation in the dressing room. There was no confrontation in the bus. In fact it was a stunned silence
Pakistan spokesman
The team has been dogged for years by damaging internal rifts and suggestions of power struggles between Inzamam and Woolmer.
However, Mr Mir denied widespread reports of any clash with the coach.
"There was no confrontation in the dressing room. There was no confrontation in the bus. In fact it was a stunned silence."
Woolmer then went to his room with a final word for his captain, telling Inzamam-ul-Haq "it is a sad thing we are parting this way".
The circumstances surrounding the defeat by Ireland have become a key part of the police investigation into Woolmer's murder.
Questioning 'routine'
Pakistan's players and management touched down at London's Heathrow airport shortly before midday on Sunday and were ushered away from the waiting media.
Woolmer's body is being kept in Kingston until an inquest is held.
In Jamaica, Mark Shields said the three squad members were questioned on Saturday to "clear up" any possible "ambiguities" given in the statements taken earlier from the team.
"Throughout this process, there has been nothing but co-operation from the Pakistan team," Mr Shields added.
Mushtaq told Sky News that police had asked "lots of guys different questions".
"It is not a big issue, just a matter of timing," he said. "It was little things they wanted to know.
"We have to follow police policies and everything is calm and OK. We are supporting the police. We are leaving and they wanted to clear everything up."
We are 110% sure [that none of the Pakistan team were involved]
Inzamam confirmed he had spoken to the police again but would not reveal any details.
"Someone asked me a question and I gave him an answer," said the Pakistan captain. "I will not tell you the question but it is nothing serious. It is not a special thing.
"He told me 'Please go home, there is nothing else'."
Detectives in Jamaica believe Woolmer probably knew his killer - or killers - as there were no signs of forced entry into his room and none of his belongings had been stolen.
Pakistan's players had already given police DNA samples and fingerprints as part of the probe into Mr Woolmer's murder.
However, Mushtaq was confident that none of the Pakistan team could be implicated in Woolmer's murder.
"God willing, I am 110% sure [that none of the Pakistan team were involved]," he said.
Two Pakistan government officials have travelled to the island to liaise with the Jamaican authorities over the investigation.
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Anupamaa
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