The advice backs the stance taken on interest rates by the Bank of England, which is expected to renew its warning that the Government is in danger of missing its inflation target in its Inflation Report due out today.
Lord Alexander's call comes after a similar appeal last Friday by Lloyds Bank's chief executive, Sir Brian Pitman.
Some economists are already labelling the unprecedented public co-ordination as an orchestrated attempt to increase pressure on the Chancellor, Kenneth Clarke, by the Bank of England's Governor, Eddie George.
Mr George was left almost high and dry three months ago when the City was convinced that he and Mr Clarke had agreed a base rate rise from the current 6.75 per cent but that Mr Clarke had changed his mind after May's disastrous local election results.
A rate rise would fly in the face of urgent calls for a rate cut from Peter Birch, chief executive of Abbey National on Monday, and other mortgage lenders who want to kick-start the moribund housing market.
Caught in the middle is Andrew Buxton, chairman of Barclays Bank, who as chairman of the Confederation of British Industry's economic affairs committee said last week that although there was no case for a cut, a rate rise would be unnecessary. Yesterday Mr Buxton said: "I don't think it is in anyone's interest to put up rates, and I don't think it would have the desired effect."
In its annual report on the British economy, the OECD said that base rates will have to rise to 7.75 per cent if the Government is to attain its inflation target of 2.5 per cent or less by the end of this Parliament.
It also implicitly criticised the new formulation of the target set out by the Chancellor in his Mansion House speech in June. The report, completed before then, suggests that "the medium-term target for inflation should ideally be below 2 per cent."
The Chancellor said in a statement yesterday that he viewed the OECD survey as confirmation of "the success of the Government's policies on a broad front. I particularily welcome the recognition that supply side reforms have resulted in a more flexible and less inflation prone economy, and the OECD's assessment of the success of the monetary framework."
Lord Alexander, unveiling NatWest's half year results yesterday, said that he "did not believe the Government was on course" for its inflation target.
"The Government will have to contemplate an increase in interest rates. It would be very disappointing if we once again let inflation get away," said the NatWest chairman.
The OECD added its voice to calls for an independent Bank. Despite the more public role the Government has given the Bank, "monetary policy in the UK remains subject to greater political control than in many other OECD countries, including the US, Japan, Germany and France. Credibility might be further enhanced by giving the Bank responsibility (possibly with legal backing) for deciding on the size and timing of interest rate changes needed to achieve the government's inflation objective."
The OECD also endorsed the Bank of England's concern about the effect of the 5 per cent depreciation of the pound in the first half of this year. If sustained, this represents "a modest unplanned easing in monetary conditions."