Top civil servant John Gieve - who is the permanent secretary at the Home Office - conceded that the new Airwave radio would not make the July deadline.
Under questioning from Tatton MP George Osborne, Mr Gieve said he hoped the system would be running in some districts in time but not in the "main district of the games".
He added: "It will affect the 'how' but we have had assurances from Greater Manchester Police that it won't affect policing.
"It [the new radio] would have allowed them to do it more efficiently than they can do it with the existing system."
Competitors dropped out
Mr Gieve's evidence came after the National Audit Office criticised a £1.47bn deal with mm02 - formerly BT - because of a "lack of competition".
That occurred because the other competitors for the 19-year contract to provide the digital radio system for the UK dropped out.
The size of the 17% profit that mm02 could gain caused committee chairman Edward Leigh concern.
He challenged Phillip Webb, chief executive of the Police Information Technology Organisation (Pito) that handled the deal, how they decided it was acceptable
He said: "You have arrived at this figure but you have only got one company bidding for this because you are locked in to this project."
But Mr Webb insisted it was "fair" in light of the sizeable risks the company would incur in developing such a system.
Labour MP Jon Trickett suggested that the Airwave system was a luxury that the taxpayer could ill-afford.
He estimated that the £180m a year running costs could provide about 3,000 extra officers a year - assuming they cost around £40,000 each.
"I know what my constituents want, after suffering a tidal wave of crime under the Home Office, and that's more policemen," said Mr Trickett.
More effective?
"We could employ even more officers if you had not decided to go down what appears to me to be a fairly disastrous track."
But Mr Gieve insisted that although the system was "very expensive" it would ultimately produce "great benefits" for the police.
Not only were more police needed but they had to be more effective too.
The radio system is intended to free up officers so that they spend less time in police stations.
It would also make it harder for criminals to eavesdrop on police activity.