Officers from nine forces drafted in to close a short-term gap in Olympics security should be able to be withdrawn “over the coming days”, G4S said today.
The private firm, which has seen its shares dive by as much as 10% following the Games security debacle, said venue security was being tightened "before the full complement of accredited staff have been assigned".
"This situation is being rectified over the coming days, which should lead to the withdrawal of police officers from those roles assigned to private security," a G4S spokesman said.
The spokesman said: "As the games get closer, security is being tightened at venues around the UK, before the full complement of accredited staff have been assigned.
"Some venues are being supported by police in the short-term while the private security workforce is being mobilised.
"We are very grateful to the police for stepping in.
"This situation is being rectified over the coming days, which should lead to the withdrawal of police officers from those roles assigned to private security."
With less than two weeks until the opening ceremony, ministers insisted the Games would be secure and dismissed the firm's failure to provide the promised 10,000 security guards as a "hitch".
But hundreds of police officers are now being deployed, in addition to the 3,500 servicemen and women who were called in last week.
Assistant Commissioner Chris Allison, the National Olympic Security Co-ordinator, said: "Nine venue forces have now deployed police officers to support security regimes at venues in their areas."
The forces involved are Dorset, Surrey, Hertfordshire, Northumbria, South Wales, Strathclyde, West Midlands, Thames Valley and Greater Manchester.
Mr Allison went on: "Whilst some of the activity police officers are undertaking was not anticipated, plans were put in place to allow us to do this.
"Forces are making sure they make the best use of their resources locally to do all they can to minimise the impact on local policing."
He added: "There is a shortfall within G4S. The military have increased their number of military personnel being deployed. We are deploying additional officers consistent with the venue security plan.
"The plan is exactly the same as it was, it is just being delivered by some slightly different people."
But West Midlands Police Federation chairman Ian Edwards said it was "chaos, absolute chaos".
The force has had to provide 150 officers per day to cover a hotel in Warwickshire where footballers are staying, he said.
"The worst-case scenario is that we end up having to find another 200 officers for the security at the City of Coventry stadium, and we've yet to find out what the shortfall is in Birmingham. It's chaos, absolute chaos.
"You shouldn't lose your local police officer because of the Olympics. Communities are suffering because a private company has failed to deliver on a contract."
Clive Chamberlain, chairman of Dorset Police Federation, said so far the Army has covered for the shortfall in G4S staff.
He said: "On a daily basis it's a lottery as to how many staff are going to turn up. The best they've managed is 15% not turning up, and on the worst occasions they have been 59% down. It's a fiasco, it's an absolute debacle.
"My biggest fear is that G4S are now panic-recruiting people to get as many people as they can into the organisation. Two weeks before the Games, we are going to have hundreds or thousands of people that are going to need to be properly vetted, that comes down to the police.
"What proper training will they have had before they start? It's very, very worrying."
Assistant chief constable Terry Sweeney, of Greater Manchester Police, said officers were called in to help "with the security operation to protect athletes staying at the main Olympic team hotel in Worsley" yesterday after the force became aware of a shortfall on Saturday.
"At no point was there a failure to provide security for the athletes," he said.
"Extra policing resources have had to be called in, but there has been a minimal impact on policing the local communities that we serve on a daily basis."
Prime Minister David Cameron said the Government had been monitoring potential Olympic problems since it took power.
Deputy Prime Minister Nick Clegg added: "It is being sorted out, it will be sorted out and we will deliver a secure Olympic Games."
Olympics minister Hugh Robertson said: "In terms of the security numbers, I am as confident as I can be at this stage that the problems identified last week and the plans brought forward very quickly to deal with it will result in the delivery of secure and safe Games."
The first competitors are taking up residence in the Athletes' Village for the London Olympics today.
The first of the Olympics Games Lanes also came into operation on the recently repaired and reopened M4, hours after the Government refused to rule out the prospect of drafting in more troops in the wake of the G4S security fiasco.
It emerged yesterday that ministers had been warned 10 months ago in a confidential report by HM Inspectorate of Constabulary (HMIC) about concerns over security.
It was following the HMIC report that a review of security requirements led Locog to increase the number of security guards to be supplied by G4S from 2,000 to 10,400 while the value of the contract more than trebled from £86 million to £284 million.
G4S chief executive Nick Buckles, who is due before the Commons Home Affairs Committee tomorrow, has admitted he may be forced to quit his £830,000-a-year job in the wake of the Olympics debacle.
The FTSE 100 Index firm has admitted that it will incur a loss of up to £50 million on the high-profile contract.
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