The poll, in which Labour's lead is unchanged at 24 points, also points to a small majority in favour of changing to a proportional voting system in the referendum on the issue which Labour has promised, although many voters have yet to make up their minds.
In a finding which contradicts the assumption of widespread voter apathy, nearly three-quarters of those polled (73 per cent) said they thought a Labour win in the election would mean "big changes", or "some changes", for the country. Only 18 per cent predicted "hardly any changes", or "no changes at all".
It seems most voters are going into the campaign proper with modest expectations of the difference Tony Blair would make as prime minister.
Mr Blair said yesterday that his manifesto "does not promise the earth" - which seems to be accepted by people intending to vote Labour. Of them, only 24 per cent expect "big changes", while 56 per cent see "some changes".
It is Conservative supporters who are most likely to forecast "big changes" under Labour - feared by 34 per cent of them. Liberal Democrats are most likely to be cynical - 26 per cent of them expect "hardly any", or "no" changes.
But the overwhelming majority of the electorate rejects the idea that there is no difference between the parties.
In a separate finding, however, most voters take a jaundiced view of Mr Blair's ability to maintain a united front over Europe if he forms the government, with 46 per cent (and 45 per cent of Labour supporters) expecting it to be as divided as the Tories.
The Independent/Harris poll suggests that there is all to play for in the referendum on electoral reform promised by Mr Blair - who is "not persuaded" of the case for change. He could come under pressure from Labour supporters, who support a proportional voting system by a margin of 44 to 31 per cent, with 22 per cent undecided.
Predictably, Liberal Democrats are most keen on change (backed by 60 per cent), while Tories are most opposed (56 per cent back the present system).
But our poll will steady Labour nerves, showing the party's lead unchanged since last week, on 52 per cent to the Tories' 28 per cent, with the Liberal Democrats on 14 per cent.
Today's Gallup poll in the Telegraph shows the gap closing by 4.5 points over two weeks, with Labour on 52 per cent, the Tories on 31 per cent and Liberal Democrats on 11 per cent.
Two other polls this week produced contrary findings - ICM showing the gap closing. while MORI showed it widening. So, while polling companies may disagree about the levels of support for each party, there is no clear evidence yet of a shift in public opinion.
The clear gainer in our poll today is Sir James Goldsmith's Referendum Party, which registered 3.2 per cent support - its highest in our polls.
This will alarm Conservative Central Office because the Referendum Party's support continues to come overwhelmingly from among those who say they voted Tory in 1992.
It is possible that The Independent/Harris poll overstates the Labour Party's lead by a few points, as it puts the Tories four points behind when people are asked how they voted at the last general election. Other evidence suggests the parties should be level pegging on this measure.
Harris Research interviewed 1,091 adults face-to-face in their homes between 27 and 31 March.