The clash came as Mr George delivered a strong defence of the Bank's inflation strategy and fired a warning shot across the Chancellor's bows about the scope for Budget tax cuts.
Mr George told the CBI conference in Harrogate that the rise in base rates had been necessary to curb a "textbook domestically-driven economic upswing" and repeated the Bank's view that some further rise may well be necessary in due course to keep a lid on inflation.
But Mr Buxton said the interest rate rise had not been necessary although he recognised the Governor's concerns about inflation and the need to act early. He went on to urge the Chancellor to bear in mind that further interest rate rises would further strengthen the pound, depressing exports and manufacturing performance.
"We should therefore not rush to interest rate rises without thinking of our exporters." Mr George said that keeping a tight grip on inflation was not enough to improve economic performance alone.
"It needs to be accompanied by prudent and sustainable fiscal policy," he added. On economic and monetary union, he said Britain did not need to be apprehensive about the euro, whether or not it joined in the first phase of a single currency. But it did need to be prepared.
Mr George also took to task those member states tempted to fudge their performance on debt and public deficit in the "hectic dash for the line" to qualify for a single currency, and their temptation "to take artificial stimulants in order to get there".