David Cameron's hopes of keeping Britain in the EU appear to be increasingly dependent on Labour leader Jeremy Corbyn after his rating tumbled by eight points since February to 21%. By contrast, Corbyn gained two points, rising to 28%.

A YouGov poll for the Times suggested that Cameron was less trusted on the EU referendum than the Opposition leader. According to the pollster, the referendum is on a knife edge with 39% support for both the Remain and Leave camps. A further 17% said they were undecided on which way they would vote, while five percent said they had no intention of doing so.

The survey indicates that 30% of voters are "definite" that they will opt to stay in the bloc while 29% have the opposite conviction. According to the poll, four out of 10 voters do not have firmly fixed views and of these, 13% do not know how they will vote.

Corbyn to make the case for staying, 'warts and all'

The grim reading for Cameron comes as Corbyn is set to make his first intervention in the EU referendum campaign. In a speech in central London, Corbyn will argue that there is a "strong socialist case" for voting to stay in.

Corbyn will say: "The Labour Party is overwhelmingly for staying in, because we believe the European Union has brought investment, jobs and protection for workers, consumers and the environment, and offers the best chance of meeting the challenges we face in the 21st century."

Despite rejecting the Lisbon Treaty in 2008 and voicing criticism of the EU in the past, Corbyn will use his speech to highlight the dangers of attempting to "blame the EU, or worse to blame foreigners" for the country's "problems". He will also reject the notion that the EU is at fault for the steel crisis gripping the UK.

EU referendum: This is what you really need to know about the Brexit vote IBTimes UK

"It is not the EU that is the problem, but a Conservative government here in Britain that doesn't recognise the strategic importance of steel, for our economy and for the jobs and skills in those communities."

Corbyn will add: "You cannot build a better world unless you engage with the world, build allies and deliver change. The EU, warts and all, has proved itself to be a crucial international framework to do that."

The campaign is officially set to begin on 15 April, with Britain Stronger in Europe and Vote Leave – chaired by Michael Gove – now the official Remain and Leave camps respectively.

Cameron's leadership takes a knock

The prime minister is currently experiencing one of the more testing periods of his leadership following the Budget fiasco and resignation of Iain Duncan Smith as work and pensions secretary, the Tata Steel crisis and the resulting fallout following leak of the Panama Papers. This has led to a sharp increase in the number of voters who think Cameron should step down after the 23 June referendum. Results from the survey showed that 31% of people said he should quit in the year after vote – an increase of 13 points.

The Conservative party has also been dogged by infighting over the EU referendum, with Cameron's decision to spend £9.3m on a pro-EU mailshot to deliver to every home in the country a particular source of tension. The decision prompted a strong outburst from Ribble Valley MP Nigel Evans, who accused Cameron of "spiv Robert Mugabe antics."

Labour currently stands three points ahead of the Tories on 34%, followed by Ukip (18%) and the Lib Dems (11%). Some 71% of Labour voters say they trust Corbyn on Europe.