The upshot is that even if the headline rate dips below the official target of 2pc in the coming months, as seems likely, it may pick up again later in the year.
This is already happening in the euro area, where headline, core and services inflation all rose in May. The ECB may have lowered rates last week, but the markets are less confident that it will follow up with more cuts soon.
Second, the outlook for the UK labour market is more uncertain than usual.
This partly reflects doubts about the reliability of the data. But some MPC members will also want more reassurance that persistent labour shortages and the large hike in the National Living Wage in April are not fuelling a so-called wage-price spiral.
Third, and more positively, the UK economy is doing better than expected.
Growth was surprisingly strong in the first quarter of the year, and the timelier business surveys suggest there is still plenty of positive momentum.
The CBI is the latest body to revise up its forecasts for the UK economy, expecting growth of 1pc in 2024 and nearly 2pc in 2025, driven by a rebound in consumer spending.
Fourthly, now the Bank is finally paying more attention to the monetary aggregates, it is only fair to acknowledge that broad money growth has picked up to a three-month annualised rate of around 5pc.
This is consistent with decent growth in activity and suggests that the risks of a nasty bout of deflation have faded.
I have not yet mentioned politics. Many have argued that Rishi Sunak’s decision to call a General Election for July 4 means we should rule out a rate cut at the next MPC meeting on June 20.
I am not convinced. Some cynics have suggested that the Bank will not want to do the Conservatives a favour by cutting rates ahead of the election, or at least that the MPC will be keen to avoid any perception of bias.
But this works both ways. If there is a clear economic case for an interest rate cut and the MPC still does nothing, the Bank could be accused of helping Labour instead.
In fact, there have been several occasions where at least one MPC member has voted to change rates during an election campaign. It is therefore still possible that others will join the two members already arguing for a cut.
However, this would need to be justified by the new data, and market expectations of a June rate cut are now extremely low. Unless this changes dramatically in less than two weeks, most MPC members will be reluctant to spring a surprise so close to the polls.
Nonetheless, whether the first move comes in June or August, there is still a powerful case for cutting rates in the summer.
To begin with, the most recent news on inflation has indeed been reassuring.
Business surveys suggest that shop price inflation fell further in May, including food price inflation. The PMI survey showed that services inflation is easing too. The stronger pound and the renewed decline in oil prices will help a little as well.
In the meantime, the labour market continues to cool.
The Bank of England’s own Decision Maker Panel survey found that expectations for wage growth over the coming year fell back to 4.1pc in May, from 4.6pc in April. No sign of a wage-price spiral there.
The starting point is important, too. The Bank of England’s official rate at 5.25pc is well above what might be considered a “neutral” level. It is also higher than in the euro area, where the overnight deposit rate is now 3.75pc.
UK rates could therefore be cut in some way and still be bearing down on inflation, especially if the Bank continues with its relatively aggressive sales of government bonds as it reverses the policy of Quantitative Easing.
Finally, the revival in economic activity and confidence is rooted – at least in part – in hopes that falling inflation will allow the Bank to cut interest rates.
The Bank’s own staff forecasts have inflation dropping to the 2pc target and remaining there or thereabouts, even on the basis of market expectations of a string of rate cuts.
If the MPC fails to deliver soon, a longer period of unnecessarily high interest rates could still sink the recovery.
Julian Jessop is an independent economist.