I've been looking at the British Social Attitudes survey* because I'm extremely boring. One of the questions is "Which party did you vote for in the 1992 General Election?" and it's interesting how the numbers changed over the course of a decade as the Tories became ever more unpopular:
1994: Conservative- 32.28, Labour- 29.26, Liberal Democrat- 12.5
1996: Conservative- 30.24, Labour- 30.90, Liberal Democrat- 9.21
1999: Conservative- 21.34, Labour- 39.30, Liberal Democrat- 9.18
In reality the Conservative vote in the 1992 election was over 40%, yet by the end of the decade at around half of thosr voters had blotted the memory of voting Tory from their minds.
A similar process is probably underway with Labour voters now.
Despite the headline I doubt that this many people are liars, it's just that they tend to subconsciously rewrite their own histories to fit in better with whatever they believe now, unless they were unfortunate enough to have been on the record about their earlier opinions at the time. This is why the vast majority of people who discuss the Iraq war now insist that they were always opposed to it, yet the opinion polls at the time showed public opinion was split more or less equally.
* It isn't as useful as it's American equivalent the General Social Survey because you can't cross reference as many variables.