Mr George told Mr Clarke that the 0.25 percentage point rise which they both agreed to implement immediately on 30 October, to the surprise of the City, might have to be followed up with further increases to keep inflation under control.
The governor said that the quarter point "might well not be enough to moderate the upswing sufficiently to restore a better-than-even chance of achieving the inflation target over the next two years".
Mr George's warning came as renewed predictions of a strong improvement in the housing market were published by Oxford Economic Forecasting, which expected that house price inflation of 7 per cent a year could bring a sharp increase in house sales in the near future.
Building societies have been predicting a sustained recovery in prices, and economists have forecasted rises of up to 10 per cent a year over the next few years. But the key piece of evidence needed to show that the recovery is strong and sustained is a move to much higher turnover in the housing market, which has not yet materialised.
Turnover has been rising at about the same rate as prices, up 7 per cent on a year ago, but from a very low base of around 1.2 million transactions a year.
However, the Oxford institute said transactions could rise "fairly rapidly in the near future" to around 2 million at the end of the decade, not far short of the previous peak.
According to the minutes of the October meeting, the Chancellor said he "certainly did not want activity in the housing market to get out of hand and would watch it closely". Activity was picking up but sales of houses in London were distorting the overall picture, which remained patchy, he said. Demand was high and supply was restricted as homeowners kept their houses off the market in expectation of further increases.
Mr George said recent evidence showed overall inflation was less likely to be below the 2.5 per cent target "for any length of time in the short run". The Government has a medium-term target of 2.5 per cent for underlying inflation, which has been stuck at 3.3 per cent year-on-year for the past two months.
In an apparent reference to the political pressure to keep rates down ahead of the election, Mr George said "given present expectations about the constraints on policy, a quarter per cent move now could have a relatively strong signal effect on the credibility of policy".
That would reduce the size and speed of the rise in rates that might eventually be necessary to make the inflation target secure and sustain the economic expansion.
Explaining the background to his recommendation of the October increase, Mr George said the need for tightening was urgent because output was growing above trend and the expected fall in price inflation had failed to happen.
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