The warning, delivered at a London conference attended by Edward Leigh, the industry minister responsible for postal services, was being seen as a further sighting shot in the Post Office's campaign to be sold off intact.
Mr Cockburn said that privatisation would give the Post Office the commercial freedom it sought. But he added: 'If the Government goes down that route we would say privatise everything together as a unitary business.'
Michael Heseltine, President of the Board of Trade, has been sitting on the results of a review of the Post Office's future ownership for several weeks.
He has been unable to canvass opinions of other Cabinet members in order to reach a decision because all his energies have been devoted to the coal industry crisis.
Ministers are mindful of the need to make an announcement. However, supposing Mr Heseltine gives the go-ahead for privatisation of the Post Office, it is unlikely that a bill would be put before Parliament until the 1994- 95 session.
Mr Cockburn said that since the Royal Mail and Parcelforce shared the same obligation to deliver to every address in the country for a uniform price they should be kept together.
As for the Counters business, he questioned how the 10,000 loss-making post offices in rural and out-of-town areas would survive without cross-subsidisation from the rest of the network.
The Post Office's stance threatens to put it on a direct collision course with the Government if Mr Heseltine goes ahead with his already announced intention of privatising Parcelforce separately.
Mr Leigh said that no decisions had been taken over the review and that the intention to privatise Parcelforce did not necessarily mean that the rest of the Post Office would be privatised.
The minister also reiterated the Government's 'non-negotiable' commitment to maintain a nationwide letter delivery service at a uniform price whatever the outcome of the ownership review.
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