In particular, it fears people are gearing up with debt that will prove to be more of a burden to repay than they expect. High inflation may have meant higher interest rates in the Seventies and Eighties. But it also meant rising prices and wages, which soon lightened the burden of mortgages, overdrafts and loans.
Now, low inflation and low interest rates mean smaller monthly payments, reducing the strain of servicing debts. But they also mean that the debts in question will weigh more heavily for longer. In other words, borrowers cannot rely on inflation to erode the debt millstone around their necks.
The Bank's deputy Governor, Mervyn King, disclosed this month that he and his colleagues are stepping up their research into what might be called the millstone effect. 'We need to do more work on this,' he said. 'The data we have are not as good as they could be.' In theory, inflation and interest rates ought to move in tandem, leaving borrowers to make one decision only: can they afford to take on the debt in question?
But the swings and roundabouts do not work perfectly. Inflation redistributes wealth around the economy, and high inflation favours borrowers and punishes savers.
As our examples below show, the same borrower - our fictional Feckless Freddie - can borrow exactly the same amount, £1,000, for exactly the same period, 12 months, and fare very differently, depending on which year in the past quarter-century he took out the loan.
Back in 1975, Freddie was actually being paid to borrow money: amazing as it may seem today, real interest rates were negative in that year, with an 11% base rate more than wiped out by inflation of 24.2% - 16 times today's cost-of-living increase.
Even in 1988, nine years into the Thatcher era, Freddie was pocketing a useful discount on his debts, courtesy of inflation. True, he was no longer being paid to borrow, as he had been in 1975. But the £101 he paid in interest was effectively reduced by £52 through no effort of his own - that is nearly 5% of the total owed.
Come 1997, and his 'inflation discount' - the amount by which the real value of his debt was eroded by rising prices - was down to £31, three% of the total owing. As Labour swept into power, things could only get worse for Freddie. And they did.
Five years on, inflation is chipping a mere £15 off the real cost of Freddie's loan. That's 1.5% of the sum owed. Freddie is far worse off than he would have been in 1975.
Our examples of Freddie's fluctuating fortunes are very simply drawn. They assume he pays the Bank of England base rate (when borrowers almost always pay more than that).
They also assume that his income has kept up with inflation, which it almost certainly will have done, provided he is in work rather than living off a pension.
But, simple though they are, they vividly illustrate the workings of the millstone effect as Freddie's debts are no longer eroded by inflation. When price increases are running at a high level, all money loses its value - including borrowed money. Thus it makes sense to owe money rather than lend it. However, low-level price increases, such as we experience today, preserve the value of money, including debts.
Those who have borrowed heavily can no longer rely on inflation to bail them out. The burden of debt maintains its weight. And that effect works even more markedly on longterm loans such as mortgages.
John O'Sullivan, economist at Dresdner Kleinwort Wasserstein, has compared mortgages in a high-inflation world with those in a low-inflation world.
Assuming inflation, interest rates, wage increases and house prices all run at 10% a year, O'Sullivan says mortgage payments will take 11.2% of the borrower's total income over a 25-year period.
But if inflation, interest rates, wage and house price increases are running at just 5% a year, O'Sullivan says the share of total income rises to 14.9%.
'Mortgage payments are initially much higher in the high-inflation scenario,' O'Sullivan says. 'But the benefit of debt erosion through high inflation outweighs the cost of a higher interest rate.'
Does this matter? Indeed, is it not rather unhealthy to let inflation subsidise borrowing? Perhaps. But the millstone effect reduces households' room for manoeuvre because people who are still paying off old debts are unable or unwilling to assume new ones.
And that means they would respond less swiftly to any future cuts in interest rates, were the Bank of England to feel the need to stimulate the economy. No wonder the Bank is urgently investigating the millstone effect. It could become a major drag on more than just the borrowers' incomes.
How Feckless Freddie fared with a £1,000 loan
1975: Having a ball on the cheap
Interest rate: 11% Inflation rate: 24.2%
Feckless Freddie owes £1,110 at the end of the year. But the goods that cost him £1,000 at the start of 1975 would now cost £1,242. Borrowing made him £132 better off.
1988: Still enjoying the good life
Interest rate: 10.1% Inflation rate: 4.9%
Freddie owes £1,101 at the end of the year. But the price of goods he bought for £1,000 is now £1,049. Inflation has chipped £49 from the real cost of borrowing.
1997: Beginning to feel the pinch
Interest rate: 6.6% Inflation: 3.1%
Freddie owes £1,066 by the year end. The price of the goods he bought has risen by £31: that's the amount that inflation has knocked off the real cost of Freddie's loan.
2002: Agonising as debt mounts
Interest rate: 4% Inflation: 1.5%
Freddie's £1,000 loan would cost £1,040 to repay. But the price of the goods he bought has risen to only £1,015. Inflation has cut the real cost of Freddie's loan by just £15.