This week we saw the release of the latest minutes of their regular monthly meetings, at which Mr Clarke yet again held out against Eddie George's demands for an extra 0.25 per cent rise in interest rates.
As there are few more important factors in the outlook for investors than the future movement in interest rates and inflation, the importance of these skirmishes should not be underestimated. With an election looming, nobody should be surprised that the Chancellor has decided to resist a rise that both the Bank and, so it is reported, the Treasury's own officials now favour.
Although no less an authority than the Financial Times has chided the Chancellor for playing political games with the economy, most of us expected little else. The economy is not in such fragile form that a quarter of a percentage point movement in short-term interest rates is going to make much difference between now and May. The recent strength of sterling, which tends to reduce inflationary pressures, has given Mr Clarke all the ammunition he needs to resist the Bank's demands.
The underlying inflation rate is still falling, and set to bottom out this summer, so the argument is really all about what happens in a year or so.
My view is that the public arguments between Chancellor and Governor are proof that the new and more open method of settling monetary policy adopted after the ERM debacle is working pretty well. That is a plus for all investors, for while the Bank may be losing the odd skirmish, the battle against inflation, which is what matters to most investors, continues to go rather well.
Indeed, the Bank itself seems to accept this in an oblique way. Its latest Quarterly Bulletin provides ample evidence that the financial markets continue to take much greater heart than before about the long-term trend in inflation. As my chart shows, interpolating the markets' longer-term expectations about inflation from the different interest rates set by supply and demand in the money markets reveals an interesting picture.
In the second half of last year, what happened was a continued decline in inflationary expectations for the medium and longer term. While everybody expects some rise in interest rates this year, whoever wins the election, looking 10 years and 15 years out, the inflationary trend looks increasingly benign. Not only are 10- and 15-year expectations of inflation continuing to fall, but they are also now converging on short-term expectations as well, at a new low level.
Implied future rates of inflation are all converging on a range around 4 per cent. By comparison, three years ago the markets were still looking for a long-term rate of inflation of 6 per cent. Credit for this is not all down to the Government by any means. Many other countries have done even better with inflation and the most powerful forces behind the decline are global, not specifically UK ones. But John Major and Mr Clarke can certainly take credit for a greater degree of credibility in their counter- inflationary policy.
Why does that matter to investors? For one simple reason - because it is the long-term rate of interest which ultimately drives the value of the stock and gilts markets. Short-term interest rate movements do affect sentiment, and some sectors of the market (eg cyclical industrial companies) more than others. But the bigger influence is the long-term interest rate.
Of course, there is nothing to say that the markets are right in their expectations, nor that the global fall in long-term real interest rates which has propelled us through the whole of the post-1982 bull market will not soon turn. But it has not happened yet, which is one reason Wall Street continues to defy gravity (though even my chartist friend Robin Griffiths at James Capel, who has called the bull market correctly all the way through, thinks that the end of Wall Street's great run is now hoving into sight).
Whether they appreciate it or not, investors have lived through a momentous period in economic history in the past 20 years. The fall in long-term interest rates and inflationary expectations, painful and protracted as the process has been in many ways, has been a necessary condition for the enduring bull market. As long as the Governor and Chancellor spend their time arguing about 0.25 per cent movements in interest rates - it is only five years since they were briefly put up to 15 per cent during the ERM crisis - the omens are still encouraging.