Splitting banks is "crazy economics"

That comes as Sir Richard Branson's Virgin Money has been mooted as a potential buyer of the good Rock and confirmed it is keeping a "close eye" on developments in the banking sector

National Australia Bank - which owns Cyldesdale and Yorkshire Banks - and Spanish giant BBVA are also said to be interested, but refused to comment.

Tesco's banking arm is also another potential bidder, although new reports suggest this is unlikely.

Chancellor Alistair Darling has insisted the Government is in "no hurry" to sell the bank off with the general election due within months.

Mr Redwood, chairman of the Tory Economic Competitiveness Policy Group, said: "This is lopsided privatisation at its worst. It is crazy economics, leaving the banking market with newly privatised large banks unencumbered by some of the usual junk loans all banks have accumulated over the years.

"It is another nasty mugging of the taxpayer, expecting us to pick up all the bills for past excess and present sloppy management."

Bank privatisation should cut the risk to taxpayers by selling as many bad loans as possible with the better loans and branches to the private sector as well as increasing competition, said the Tory MP for Wokingham.

Newcastle Central MP Jim Cousins, who sits on the influential Commons Treasury committee, said Northern Rock should not be split up but the consequences had to be dealt with.

The likely withdrawal of Guarantee guarantees and strict trading restrictions on the Rock imposed by European competition chiefs meant it had to be sold to prosper, said the Labour MP.

He expressed hope it would be bought by a company willing to develop it as an independent brand, but warned it would not be sold "at top whack".

And that could see taxpayers that have supported the bank and tens of thousands of Rock customers lose out.

Some 90% of the mortgages held by the bad bank are in fact not in arrears, but Mr Cousins said they could be sold on with customers not treated well with Governments unwilling to be patient in the face of the huge public deficit.

"There is a risk of the historic mortgage book being cherry-picked and the best bits of that being dumped," said the MP who suggested taxpayers could get their money back and even make a profit if a longer-term view was taken.