At the heart of the radical plan is that Halifax should be supervised by the Bank of England, as banks are. This is a lighter supervisory regime than that of the Building Societies Commission.
While Halifax, with pounds 62bn of assets, maintains it would be content to remain under the supervision of the Bank and the BSC, in reality it would be impractical to conform to two sets of rules.
A Bank spokesman said: 'In principle there is nothing to stop us from supervising the Halifax. It is a question of what the Treasury and Parliament want.'
If the big building societies were allowed to transfer to Bank supervision, the BSC would be left to look after the smaller societies. Experts believe it might become redundant. The BSC was unwilling to comment.
Essential to the Halifax initiative is that eligible societies should be allowed to continue to call themselves building societies within the UK. Halifax wants to be able to refer to itself as a bank overseas. That would enable it to raise money on equal terms with the high-street banks, yet retain the public approval and protection from unwanted takeover that mutual status confers.
Last week Jon Foulds, Halifax's chairman, told the society's annual meeting: 'At present your board continues to believe that the Halifax can best serve its members' interests as a building society. But we need a realistic outcome from the Treasury review of the Building Societies Act. We will need wider access to world banking markets to enable us to meet forecast customer needs.'
The Treasury review is due to be completed in the next fortnight and published immediately after Parliament's Whitsun recess.
David Gilchrist, Halifax's general manager in charge of corporate development, said: 'Bank status would give us much more fund-raising power in areas where they haven't heard of building societies. And the banks have no advantage over us in terms of our credit rating.'
Abbey National is strongly opposed to Halifax's scheme precisely because it had to surrender building society status in 1989, when it converted to become a public limited company and floated its shares on the London Stock Exchange.
That brought Abbey under the Bank of England. It is technically a bank and can no longer call itself a building society.
An Abbey spokesman said: 'You can't have your cake and eat it. Riding under the hat of mutuality is all very nice, but at the end of the day if they want to behave like a PLC they should become a PLC. After all, their profits are a third bigger than ours. We are quite adamant about this: if they want broader powers, they should go through the same route as we had to.'
Neither the clearing banks nor their trade body, the British Bankers Association, were willing to comment on what would be a significant threat to their commercial position. Banks have moved increasingly into the mortgage market in recent years.
Mr Gilchrist said that Halifax had not approached any of the other big societies to lobby the Treasury.
A spokeswoman for the Nationwide, the second-biggest society, said: 'We wouldn't want to comment on the Halifax's plans, except that we have no plans to convert and we have no concerns about how we are regulated.'
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