The reasoning behind the claim - unofficial, of course, because these matters are politically charged and public statements are dangerous for careers - is that travellers within identifiable and well travelled routes, especially commuter networks, will gain significantly. They will have the benefit of better and more focused railway management, as the 25 train operating companies are franchised out to the private sector.
But those travelling cross-country on routes passing through more than one franchise area will find their services deteriorating because of the complexities of operating such a fragmented network.
This case cannot be proved one way or another until several years after privatisation, and it appears to be based mainly on gut feeling and experience rather than measurable data. But it is one of a number of claims made recently by railway insiders that buttress the public belief, shared by many MPs, that privatisation will end in tears.
Another suggestion that must have been equally unwelcome to Sir George Young, Secretary for Transport, was made this week by a senior but anonymous railway executive speaking to business journalists. It was that the Government would likely raise little more than a third of the pounds 9bn value of the railway's assets through the sale, and would probably receive only a quarter of the pounds 6bn asset value of Railtrack when the company that owns the railway infrastructure is floated on the stock market next spring.
The main reason put forward was that the Government was pushing the flotation through in too much of a hurry and would not get full value from the City.
This is in fact one of two distinct strands of argument about privatisation that have been interweaved, often confusingly. The first is an objection to the structure of privatisation the Government has chosen, which results in forecasts of poorer service and higher subsidies. The second amounts to saying the privatisation now under way is being badly handled.
Most agree that many peripheral British Rail businesses, including engineering and maintenance workshops, never had any reason to belong to BR, which used to accrete such operations like some out of control and badly managed conglomerate.
The controversy all along has been about the decision to separate operation of passenger services from ownership of the rolling stock and of the track.
Leaving aside the less controversial freight and parcels operations, the new railway comprises 25 train operating companies (Tocs), three rolling stock leasing companies (Roscos), which own the engines and carriages, and Railtrack. The most powerful of the many criticisms made of this arrangement is that it will produce a railway of nightmarish complexity, in which subsidies will continue to be pumped in one end and private profits pop out the other.
Unfortunately, while the case against the form of privatisation the Government has chosen reads compellingly, it is yesterday's argument.Legislation to allow the changes has been on the statute book for several years, and the sale process is beginning to look irreversible, even if there are hiccups from time to time - such as a court challenge next week by the Save our Railways campaign to the legality of the minimum service standards set by Roger Salmon, the passenger services franchising director, or the row over Resurgence Railways' bid for the Great Western franchise.
Even Labour's opposition to rail privatisation does not go as far as tearing up the whole structure to start again from scratch. That would be tough, since the agreement this month to sell the Roscos for pounds 1.8bn has in one go brought in approaching half the likely privatisation proceeds.
As for the argument that pounds 9bn worth of railway system is being sold for a fraction of its worth, the asset numbers are a red herring. The Government has used a rather arbitrary asset valuation to set the charges to be levied between the various parts of the broken-up railway empire. But the asset figures bear little relation to the way the railways have to be valued as a business.
It is not the discrepancy between asset values and likely sale prices that matters. As with any sale to the private sector, the proceeds will be what the market will pay. This is where the old guard in the railways has a good point.
The timetable of the privatisation is being driven by politics, because the Government wishes to sell the bulk of the railways well ahead of the election. This is both to bring in the revenues to help with the Budget arithmetic this year and next and to make it hard for a Labour government to reverse the process.
The management of Railtrack, which is now quite separate from British Rail, is keen to see a 100 per cent sale take place well before the election, so there will be less chance of Labour retaking control.
But the sale, if it goes ahead as scheduled between April and June, will be after a mere two full years as a separate company.
Buyers will be well aware of the pressure to sell quickly, and that is a recipe for getting it at a knock-down price. Similarly, the pressure to sell the operating franchises in a hurry is virtually guaranteed to worsen the terms for the Government.
In the bad old days, governments wooed voters with tax giveaways and economic booms, ignoring the inflationary damage because it did not emerge until after the election. Kenneth Clarke seems to have resisted the temptation in this week's Budget.
But the Government is repeating much the same mistake in its privatisation programme, by allowing politics to determine the pace at which it sells the railways. It is taxpayers and travellers who will be left to regret at leisure afterwards.