A week, never mind five years, is a long time in politics and much has changed in the often Machiavellian world of government since then. Following an elongated farewell tour of his own, Blair finally handed over the keys of Number 10 to Gordon Brown who, with hindsight, might not have accepted them so readily having presided over the MPs'
expenses scandal and the worst economic downturn in 60 years.
Against this backdrop and with the nation preparing to vote in an election being billed as the biggest in a generation, Bremner has embarked on his Election Battlebus Tour. In the run-up to polling day, the 48 year-old impressionist is travelling up and down the country offering his take on the characters and events dominating the news.
He's been described as a "one-man opposition party" and his new show blends his impressive repertoire of characters with a political Q&A session which he hosts with a panel of mystery guests. "It's not just about the comedy, I want to give people a chance to get engaged which is why I'm doing the Q and A," he says. At his gig in Sheffield this week he was joined on stage by Labour veteran Tony Benn and Doncaster's outspoken mayor Peter Davies who ended up criticising his own councillors by suggesting they weren't up to the job.
His tour rolls into North Yorkshire later this month for a sell-out show in Harrogate, a town that Bremner remembers from his childhood.
"I went there as a kid. I was taken to the theatre when I was about six by an enthusiastic aunt to see a production of Dr Faustus. I couldn't make head nor tail of it, but I liked Harrogate."
Bremner is arguably Britain's sharpest and best known impressionist and since cutting his teeth on Jimmy Cricket's TV show And There's More 25 years ago, he has rarely been off the screen. From the Bafta award- winning Rory Bremner – Who Else? to the ever popular Bremner, Bird and Fortune, which is still going strong after 13 years.
His talent for mimicry began at school before he honed his skills on the London Cabaret circuit while studying French and German at King's College. After his initial breakthrough, he went on to provide voices for Spitting Image in the 1980s. Since then he's made the transition from light entertainer to heavyweight political satirist and now writes for the broadsheet newspapers as well as making regular appearances on The Andrew Marr Show.
He's adept at lampooning our political leaders although he feels politicians and some of the issues have become more prosaic. "Politics now tends to focus more on the nitty gritty. The economic situation, for instance, is very technical and to turn that into comedy without making it sound like a lecture is actually quite hard. I've always been interested in politics but it can be very intense and detailed, politicians are skilled at manipulating facts and figures, so instead I try and make nonsense of them."
Sometimes he's aided and abetted by the politicians themselves, as happened when the story about MPs' expenses emerged. "When you've got an MP claiming money for a duck house, it goes beyond satire, you just couldn't make that up. It was like Westminster had suddenly become the Big Brother house."
This year's election is the first where there's been a series of televised debates. We've already had the first instalment with the Chancellor Alistair Darling and his would-be successors George Osborne and Vince Cable, and next up are the three main party leaders. However, Bremner believes the debates won't tell us anything we didn't already know.
"We are getting closer to becoming an X-Factor society, which is an exercise in hype, and increasingly politics is about marketing, whether it's ideas or people. But we aren't going to have an election held on primetime TV with David Cameron singing cover versions of Michael Jackson songs – or at least I hope not."
Bremner has been at the heart of political comedy in this country for a long time now and his voice can morph effortlessly from his own into Tony Blair's and William Hague's in a single sentence. But some of the politicians he has enjoyed sending up over the years will no longer be in Parliament after the election. "Most my favourites are standing down, people like Michael Howard who is going into the 'twilight of my career where I like it best' and John Prescott," he says, going into character.
Another two political figures whose shadows have loomed large during the past 10 years are George Bush and Tony Blair, both of whom have come in for stick from Bremner. "What we learned from them is how dangerous it is when we have leadership based on belief, not religious belief, but in Blair's case the belief that he was right. He would say things like, 'I might be wrong, but this is what I believe' and hundreds of thousands of people died on the basis of that," he says.
"Through this extraordinary cult of personality Blair and Bush, almost single-handedly, created this situation where we went to war without a UN mandate, which is unprecedented in our lifetime."
The subsequent rise of Barack Obama to become the first black President of the United States led many people to believe we were witnessing a change in attitude among Americans, but Bremner isn't so sure. "Politics is a slow burn and the strange thing about Obama is he was swept to power on the slogan 'Vote for change' and when he tries to do it, people turn round and say, 'No, we don't want that.' People like the idea of change more than the reality."
He points to the fervent opposition among some Americans to President Obama's healthcare reforms. "I think some of it is racist and some of it is a hatred of anything that smacks of socialism, they still think the NHS is a communist plot. It's an abject lesson in showing that while people can be inspired to vote for change, when it comes down to it, they don't actually like it."
But despite such apparent cynicism he does believe in the simple
democracy of the ballot box and the power it gives people.
"Come election day on a wet Thursday in cold church halls up and down the country, people will be casting their democratic right to vote – and there's something sweet about that."
n Rory Bremner plays Harrogate Theatre on April 15.