Ed Miliband has come under attack from yet another unexpected quarter. Appearing on ITV’s The Agenda, the opposition Labour leader appeared to be taken by surprise when singer Myleene Klass criticised his plans for a tax on properties worth more than £2m.

As Miliband sought to defend the so-called mansion tax as a principled way of raising extra funding for the NHS, Klass said the levy would hit “little grannies” living in modest homes in London rather than the super-rich Miliband claimed to be targeting.

“What is so disturbing is the name in its own right: ‘mansion’. So immediately you conjure up in your head these Barbie-esque houses … but in London, which is where 80% of the people who are going to be paying this tax actually live, the south-east of England, have you seen what that amount of money can get you? Often it’s like a garage,” she said.

“When you do look at the people who will be suffering this tax, it’s true a lot of them are grannies who have had these houses in their families for a long, long time. The people who are the super-super-rich buying their houses for £140m, this is not necessarily going to affect them because they have got their tax rebates and their amazing accountants. It’s going to be the little grannies who have lived in those houses for years and years.”

Miliband, who initially appeared to be taken aback by the force of her onslaught, fought back. “The values of my government are going to be different to the values of this government,” he said. “I say bring on this debate. I think it is a principled view that those with the broadest shoulders should pay the biggest burden. I think that is a decent, right principle and that is not happening under this government.”

An increasingly exasperated Klass retorted: “Is that your only option? You may as well just tax me on this glass of water. You can’t just point at things and tax them.”

She was supported by fellow guest, former ambassador Sir Christopher Meyer, who said: “You’re going to screw me royally.”

As the row continued, viewers took to Twitter, with one writing: “You know it’s gone truly surreal when Myleene Klass goes full Paxman on Miliband.”

Miliband later responded on Twitter, posting: “Here’s why our NHS needs a mansion tax. It’s Pure and Simple”, a reference to one of Klass’s biggest hits with Hear’Say, along with a link to a Labour document detailing “six things you need to know” about the mansion tax.

Ed Miliband (@Ed_Miliband) Here’s why our NHS needs a mansion tax. It’s Pure and Simple. http://t.co/ol6eRj5aAW

These included the claim that the tax would raise £1.2bn, which would go towards the NHS.

The document said that “the vast majority of houses, even in London, are worth far less than” £2m, and pointed out: “The £2m threshold will rise in line with the average rise in prices – so the number of properties paying the tax will not increase.”

Klass had claimed that “later on, when fiscal drag kicks in, we’re all going to be paying it”.

Following the spat, bookmaker Coral gave odds of 5-1 that Klass would become the next presenter of the BBC’s Newsnight, 20-1 she would become a Tory MP, and 33-1 that she would become a Labour one.

Meanwhile Savills estate agents claimed the threat of a mansion tax after next May’s general election was putting off potential buyers of £2m-plus homes in London.