If David Cameron genuinely believes "Red" Ed Miliband is a socialist then a new poll suggesting the public are far to the left of Labour and want state control of key sectors of the economy, will be enough to provoke nightmares of a Marxist revolution in Downing Street.

According to the poll, voters support state-imposed price controls on the utilities, re-nationalisation of the railways and Royal Mail, an end to private cash in the public sector and even state power to regulate rents.

But perhaps more worrying for the Tories is that, when asked, voters said they didn't believe either party was on the side of working people, suggesting they want to see even more radical policies.

And that could lead to pressure on Miliband to come up with even more populist policies such as his energy price freeze which has struck such a chord with the public - the poll showing 74% back such controls.

And it gets worse for Cameron. Even Tories support some of the more radical proposals such as state control of transport and utilities and almost 80% of voters feel they are not personally benefitting from the economic recovery, with even 70% of Tory voters feeling the same way.

The YouGov survey for the Centre for Labour and Social Studies (Class) think tank was carried out at the end of last month as the full impact of the political party conferences and subsequent debate over energy prices hit home.

It found huge opposition to private sector involvement in the public services, with an overwhelming 12 to 1 against the NHS being run by the private sector; 67% in favour of Royal Mail being run in the public sector; 66% backing nationalisation of railway companies; and 68% in favour of nationalising the energy companies.

The poll will be a boost for the Labour Party, showing twice as many people see Ed Miliband (32%) as more on the side of working people than David Cameron (16%). However the survey also found that a greater number of people (38%) don't see either leader as being on the side of working people.

The poll suggested big support for Labour's policy to freeze energy bills for 20 months, with 74% of people in favour of governments having the power to control energy prices. But the poll also suggested the public would like Labour to go further - nearly three quarters of people think the government should also control transport costs.

The poll also found 45% of the public believe that the state should have the power to control private rents, against 43% which opposed to the idea.

The findings will come as a genuine shock to politicians on all sides as they suggest the public is demanding far more radical, left-wing action to control the economy and utilities than any of the big parties are currently offering.

It will encourage some to press Labour, in particular, to go even further with its plans to control key sections of the economy, way beyond what Ed Miliband or Ed Balls are contemplating.

And it is likely to dismay the Tories whose claims that such policies would take Britain back to the bad old days of nationalised industries and state control, seem to be falling on deaf ears.

But, if the findings continue to be borne out as the general election campaign moves into top gear, and if Labour takes them to heart, it could spark the sort of ideological debate which Britain has not seen since the late 1970s and 1980s - for good or ill.