At the beginning of this month, a poll found 53 per cent of Britons would vote against joining if a referendum were held now. Only 29 per cent would vote in favour while the rest said they did not know.
But yesterday, a Gallup poll showed that four-fifths of the electorate believed it was inevitable that Britain would join the euro "sooner or later".
Equally, 58 per cent recently told ICM that Britain could not afford to stay out of the euro if it proved to be a success.
Moreover, there are clear signs of flux. Opposition rose after Britain was forced out of the euro's predecessor, the exchange rate mechanism (ERM), in 1992. And it ratcheted up again in the wake of the banning of British beef from European markets in 1996.
The same effect has been seen in recent weeks. When the spectre of European tax harmonisation was raised in November, opinion once again swung against the euro.
What the pro-single currency campaign needs is good news from Europe. Lower mortgage rates might, for example, prove an attraction; yet so far only one in ten of us recognise it as such.
And, of course, the pro-single currency campaign needs the backing of the Government. Until recently, there were signs of a slow drift in favour of the euro.
A 27-point lead for opponents of Economic and Monetary Union (EMU) just before last year's general election had dropped to 19 points by September. But that gain largely disappeared after the tax harmonisation row.
This Government makes rather friendlier noises about Europe than the previous Conservative one. But it will need a far more clear and sustained lead from ministers if public opinion is to be changed.
The Government, of course, will worry about the media. Yet whether individual newspapers have much influence on their readers is doubtful.
After all, readers of the largely pro-European Mirror are less keen on a single currency than are those of the Eurosceptic Daily Telegraph. What appears to matter is not how newspapers slant the news, but whether the news they have to report is good or bad for the single currency in the first place.
The challenge for those who wish to join the euro is to make sure the news is good.
John Curtice is deputy director of the ESRC Centre for Research into Elections and Social Trends