The answer to that question is central to future interest rate decisions. The majority view on the MPC was that sterling had, month after month, failed to weaken as expected. This made it more likely that inflation would fall below the Bank's central forecast.
On the other hand the lonely minority view of Mervyn King was that: "The benign effects on inflation of the rise in sterling and falls in import prices would be wearing off as domestic activity recovered."
The deputy governor clearly holds to the view in the last Inflation Report that there is a danger the pound will dive far more sharply than the gradual decline pencilled in by the Bank's economists.
The difficulty in forecasting whether the exchange rate will fall is that nobody entirely understands why it rose so much in the first place. The pound is only about 5 per cent higher than its central level during the period of Britain's membership of the Exchange Rate Mechanism, but has climbed a staggering 26 per cent from its low point in 1995.
There are three main candidate explanations for the massive rise in 1996 and 1997. One is that the economy's fundamental strength has improved so much that the UK warrants a higher exchange rate.
Michael Dicks at Lehman Brothers said: "The pound's fundamental strength might be a bit better than it was. That is why the trade performance has been so good." In contrast to the late 1980s, the trade position has not got dramatically worse - at least until now.
A second argument is that UK interest rates were higher than rates on competing dollar, euro and yen assets, partly reflecting the position of the economy in the business cycle. UK rates have been the highest in the G7 for most of the 1990s and were climbing until last summer because growth was so buoyant.
A third is the "safe haven" argument that sterling was stronger to the extent it provided investors with shelter from Europe's monetary union. And indeed, any piece of news suggesting the chances of British entry have receded tends to be greeted with a knee-jerk rise in the pound-euro exchange rate.
All of these could have played a part in the pound's appreciation, but each has different implications for the outlook now. Not surprisingly, analysts' opinions vary widely.
Paul Krugman, the eminent Professor of Economics at the Massachusetts Institute of Technology, is sceptical about the euro's prospects for recovery against both sterling and dollar because he believes the ECB and member governments have done too little to stimulate growth. "The euro area has a deflationary bias," he said. "Where is the growth going to come from?"
He also argues that the architects of the single currency made a strategic mistake in starting it off at a value so close to parity with the dollar. "This gives a parity of one a psychological salience that it does not deserve on any fundamental economic grounds, and makes it hard to conduct a rational monetary policy," he said.
His views appear to be shared by the US administration, which in recent months has pressed Europeans to take up some of the burden of keeping the world economy afloat. Most of the appreciation of sterling has been against the euro and its predecessor currencies; the pound-dollar rate has been remarkably stable.
Paul Meggyesi, a currency expert at Deutsche Bank, agreed that the upturn in the British economy would buoy the pound, regardless of this month's rate cut. "If the UK economy is on the up and leading Euroland, then the euro-sterling rate is not about to turn around," he said.
However, many City analysts think the euro could be gaining ground against sterling in six months' time, with growth on the Continent now starting to pick up.
According to Paul Mortimer-Lee, chief economist at Paribas: "The pound's strength reflected the economic recovery." Signs of renewed growth in Europe will now take sterling lower against the euro, he predicted, while the expected increase in US rates by the Federal Reserve will also weaken it against the dollar in the short term.
Michael Saunders, an economist at Salomon Smith Barney, also predicts the pound will decline gradually, largely because he expects the MPC to continue cutting interest rates to keep the UK economy afloat. "People do not appreciate how severe the drag on growth and inflation from the strong pound will be," he said.
Many also expect sterling to weaken further against the dollar, as it did yesterday, thanks to the likely increases in US interest rates. The Fed is expected to raise its key policy rate to match the UK's 5 per cent as early as next week. Mr Mortimer-Lee said: "In the longer run the aim is to slow the American economy down, which will hit the dollar. But the rate crossover with the US is why a lot of people are now talking about sterling weakness."
But even among those experts who agree with Mr King's analysis that the outlook for sterling is weaker, there are differences of view about how far and how fast it could fall. A gentle decline would be welcome; a steep fall might require an increase in interest rates to keep inflation on target.
As members of the MPC have been at pains to emphasise, they are not targeting a weaker exchange rate. The only target is the inflation target. However, the committee's debate has made the pound the focus of attention. Its fortunes on the foreign exchanges hold the key to interest rates.