A Tory stronghold in London could swing Labour as local voters are frustrated about the state of public services and the cost of living crisis. Wandsworth is known for its comparatively low council tax, but some residents say they would prefer to pay more for better public services.

Recent polling has predicted a shock Labour swing in South London borough at Thursday's local elections, The borough has been controlled by the Tories since 1978 and was once former Prime Minister Margaret Thatcher's favourite council.

In a fresh map of what political control could look like in London after voters head to the polls on May 5, forecasters at Britain Elects, the New Statesman's election calendar, have predicted Wandsworth will turn red. Putney local Pam, 74, says she voted Labour at the last election and will again this week.

Speaking to the Local Democracy Reporting Service, she called services in Wandsworth "abysmal" – particularly older people's housing along with services for disabled people and children. She said: "The Tories have the lowest council tax, and you only get that by having fewer services. And they spend that on the things that can be seen."

Bernadette Curry and her partner David Sean Robinson, both 64, have already voted Labour by post. Bernadette said: "I'd rather pay more council tax and get better services." She added: "I just think it's appalling the fact that there's all these foodbanks and people just seem to be happy to live with them."

Glyn Jenkins, 67, is also planning to vote Labour. She said: "I think they're more caring, they're more inclusive and I've never trusted the Conservatives." She added: "Partygate hasn't helped."

But uncertainty over what policies Labour offers and criticism of Keir Starmer's leadership are turning other voters away from the party. Local resident Mary has voted Labour before but says she is not voting in the coming elections. "I don't know what Labour stands for anymore," she said. "I feel that lately Labour has lost the plot. It doesn't stand for the working class anymore."

Other locals say they aren't planning to vote because they haven't heard much about the elections. Anthony, 31, said: "I probably won't vote this time because, to be honest, I don't know too much about the ones in Wandsworth. I've not seen too much."

Tory control of the borough is encouraging other residents to keep voting for the party. Local resident Tommy said: "They're the best on the whole. They keep council tax down. I have more trust in them." Olu, 83, has always voted Tory and plans to vote for the party again. "I have more trust in them," he said.

Local politicians say council tax and the cost of living are the key issues for voters ahead of the election. Wandsworth Conservatives say the borough's services are among the best in London, and that they have helped with the cost of living "by cutting council tax this year, and freezing it last year".

David Jones, group agent of Wandsworth and Wimbledon Conservatives, said: "The council is also debt-free, unlike many neighbouring Labour-run boroughs, meaning every single penny of resident's money can be spent on service provision. Residents have been telling us they appreciate this competent, business-like approach to running their council, built up over four decades, and we are hopeful that this will be rewarded at the ballot box."

But Wandsworth Labour leader Simon Hogg says anger over partygate has been raised repeatedly on the doorstep. He said: "Life-long Conservative voters have told us they are upset over Boris Johnson breaking his own lockdown rules. People don't think it's fair that they made sacrifices while those in power broke the law."

He added: "Council tax is always a big issue in Wandsworth elections. Both parties have pledged to keep the same low council tax. It's the fair thing to do – council tax hurts renters, older people and those on low incomes." It's an election which he believes will be "right to the wire". He said: "The result will come down to a few dozen votes in a few key wards."