Should Theresa May step down as prime minister? If so, who is best placed to succeed her? Should the UK hold EU elections?

These are the sort of questions Conservative councillors are being asked as they are otherwise engaged in a local election campaign.

And one Labour councillor. Jane Milner-Barry, was sent the survey being conducted by Survation, which seems to have mistaken her for a Conservative.

She said: “When I saw it I sent it round to my colleagues, but none of them had received it – it was just me. I thought perhaps I’d crossed the floor to the Conservatives in my sleep.

“Maybe Survation saw I have a double-barrelled surname and thought I must be a Conservative, though I suspect it’s just some sort of computer glitch.”

Coun Milner-Barry said the questions were about whether the prime minister should resign. And, if she should, whether they thought Boris Johnson would be best placed to lead the party – and it also offered a choice of a number of contenders to the top job in the national party.

It also asked the councillors' opinions on Brexit, and whether EU elections should be held.

Survation said it would not normally comment on who commissioned a survey and that sometimes organisations publicised the results when they were completed.

The organisation did not respond to a further request for comment.

The Conservative Party’s head office in London said the party had not commissioned the work to be done.

Billionaire Lord Ashcroft, a life peer and former Conservative vice-chairman is also well-known for commissioning polling on political subjects, and particularly attitudes in, and towards the party.

His company also did not respond to a request for comment on whether it had paid for the survey of party councillors.

Whoever paid for the poll, it seems at least some Conservative councillors in Swindon were not thrilled to receive it in the middle of a crucial local election campaign.

A spokesman for Swindon’s Conservative cabinet said: “There is a tangible sense of frustration and growing anger brewing amongst the electorate and these sorts of shenanigans do nothing to help that.

“On May 2 voters will be going to the polls to vote for the future of their local council.

"Whilst the Westminster bubble obsesses over identity politics, the Conservative administration here in Swindon is committed to ‘business as usual’ , including a focus on delivering our major regeneration projects.

“People want to see their vote translated into practical reality and our manifesto continues to deliver economic prosperity through investment and regeneration.”

The spokesman suggested that some in the party here are finding the government’s well-publicised difficulties and rifts over Brexit a distraction from its work in the town, adding: “Usually, local elections are fought on local priorities.

“Although local issues remain very prevalent, the usual topics of parking, potholes and planning are being somewhat side-lined by Brexit and leadership battles are a step too far for most people to engage with or even be interested in at this time.

“Up and down the country, Conservative-run councils are keeping taxes low and running efficient services, as well as investing in the future. In Swindon, we remain committed to providing good value for residents and to having an exciting and ambitious vision.

“We hope that people can identify that local Conservatives are doing a good job and share our long-term vision for the future of our wonderful town. Local elections are about local issues and who can do the best job for the community.”

But Labour councillors, who need to gain five seats at this election if they hope to be able to take control at Euclid Street in May say this survey shows the party as a whole is divided, and distracted.

Leader of Swindon labour group, Jim Grant said: “It is curious that two weeks before important local elections Conservative councillors are being asked about who they would prefer as their party leader. It doesn’t suggest a strong and stable party ready to fight for the country, but rather a party thinking about its own political fortunes.

“This country is desperate for some decisive leadership to get us through Brexit and back to important issues like doctors surgeries, schools, local services and the hospitals. I really hope we can soon get a government that focusses on these kinds of important issues, rather than be introspective about what is in their own political interests."