A Tory minister was skewered by a BBC presenter over Rishi Sunak’s claim that the UK is heading for a hung parliament at the next election.

Health minister Maria Caulfield struggled to answer as Justin Webb pointed out the major flaws in the prime minister’s argument.

Sunak has said an analysis of last week’s local elections, in which the Tories lost nearly 500 seats, showed Keir Starmer will not win a majority and will need to be “propped up by the SNP, Liberal Democrats and Greens”.

That was a reference to a projection by the polling expert Michael Thrasher, who said the results suggest Labour’s lead over the Conservatives is just seven points, well short of what opinion polls have been saying for months.

However, other polling experts pointed out that Thrasher’s forecast was based on the assumption that Scotland – where there were no local elections last week – would vote the same way it did in 2019, when Labour won just one seat.

On Radio 4′s Today programme this morning, Webb told Caulfield: “Let’s look at what you and the prime minister are depending on.

“Number one: it’s not a prediction, it’s a projection based on these results. In other words, if these results were replicated, this would be the result in a general election. But people vote much more for third parties in local elections than they would in a general election.

“Number two, how many seats under this projection, would Labour win in Scotland?”

Caulfield replied: “Well I think because there were English local elections it doesn’t touch on the Scottish result.”

Webb then told her: “It assumes it would be the same as last time, so one seat. Do you seriously think that’s probable, that Labour will only win one seat in Scotland?”

Avoiding the question, the minister replied: “Polls are just projections and the polls were clearly wrong ahead of these local elections.”

But Webb said: “So do you believe that in Scotland, Labour will only win one seat at the next election? Is that the working assumption of the prime minister, because that seems to be it?”

The minister said: “These are not our analysis, and the BBC did their own analysis as well and showed it will be a hung parliament based on these results.”

Webb then told her: “But that’s the point, isn’t it? Based on these results, but nobody is suggesting that these results would be replicated at a general election. The experts aren’t suggesting it.

“I put it to you that the prime minister, if he is suggesting it to his own side, he’s taking them for fools.”

But Caulfield said: “What we can see from these results, is that people are not switching to Labour. Labour did not get the results in places like Teesside or Harlow that they were expecting, even though they threw the kitchen sink at some of those.

“Our voters are tending, at the moment, to stay at home. They don’t want a Labour government.

“The polls that were saying we would lose by about 20% did not materialise in London, did not materialise with Andy Street in the West Midlands, and we had some good results as well.”