Jean-Claude Juncker, the incoming president of the European commission, has rejected out of hand any attempt by David Cameron to “destroy” the fundamental rules of the EU on free movement of people.

In an echo of the remarks by the outgoing president José Manuel Barroso, who warned that the prime minister is making a “historic mistake” on the EU, Juncker said on Wednesday that he would not compromise in an “irresponsible way” on rights that date back to foundation of the EEC.

The intervention by Juncker, at the European parliament in Strasbourg, as MEPs approved the appointment of his new commission team, came as a new poll showed growing support among UK voters for continuing membership of the EU.

The Ipsos Mori poll, commissioned by the London Evening Standard, found that 56% of voters would support UK membership while 36% would vote to leave if a referendum were held now. The poll shows support for the EU has risen since the issue returned to centre stage with the rise of Ukip after the PM suggested in the summer of 2012 that he would support a referendum on EU membership. In November 2012, five months after Cameron floated the idea of a referendum and two months before he formally committed himself to one, Ipsos Mori found 48% of voters would like to leave the EU while 44% would support membership.

The latest poll is a mixed blessing for pro-Europeans. It shows that 43% of voters either broadly support Britain’s EU membership terms (29%) or support the idea of the UK joining with other member states for closer integration (14%). But the poll also found that 51% of voters want Britain to be a member of an economic community with no political links (34%) or would like to leave the EU altogether (17%).

Juncker said he would like to help secure a “fair deal” with Cameron if he were to put a package of reforms to EU leaders after a general election win. But the incoming commission president brushed aside recent suggestions from government sources that restrictions should be imposed on migrants from current EU states.

Speaking at a press conference at the European parliament, Juncker said: “As far as the freedom of movement is concerned ... I do think this is a basic principle of the EU since the very beginning and I am not prepared to change this because if we are destroying the freedom of movement other freedoms will fall in a later cause. So I am not ready to compromise in an irresponsible way.”

But Juncker said that any EU leader was free to table proposals to the European Council – the body that comprises the leaders of the 28 EU member states. He added: “We want a fair deal with Britain and it has to be seen how far reaching the compromises can be.

“I am not in a situation to tell you exactly what the British government will propose and so I am not in a position to tell you what the European commission will deliver as an answer to a British request. But this is not as dramatic a question as it seems. Believe me, it is not as dramatic as it seems.”

Cameron is expecting to face questions about his reform plans on the margins on an EU summit in Brussels today and on Friday which will formally discuss climate change, economic growth, the Ebola crisis and Ukraine. Herman Van Rompuy, the outgoing European Council president, has said that he would like EU leaders to agree to cut the EU’s carbon emissions by 40% below 1990 levels by 2030.

Cameron is planning to shame fellow EU leaders over their dinner on Thursday night into stepping up their response to the Ebola crisis by ensuring that the combined contribution of all 28 EU member states amounts to €1bn and that 2,000 workers are sent to west Africa.

Britain has contributed £125m (€156m) to its former colony Sierra Leone. The prime minister will say that Britain is contributing €40m ahead of the EU’s largest economy, Germany, four times more than France and 50 times more than Spain, which “with the cases they have had in Madrid have got a real experience of the challenges presented by Ebola”. The total amount pledged by EU states so far amounts to €750m.

Alisdair McIntosh, director of Business for New Europe, said of the new poll: “Many of the public recognise the important economic benefits of staying within the EU. Politicians are mistaken if they think people just want to hear ever-louder Eurosceptic rhetoric, especially at a time of economic and political uncertainty. This only increases cynicism about the major political parties.

“Politicians need to lead from the front, not shout from the back. They need to set the agenda, and reflect the importance of EU membership to business and the economy. The way to promote prosperity in Britain is to secure realistic reforms of the EU. The government should fight for the reforms that matter most – those that will create growth and jobs.”

• This article was amended on 23 October 2014. An earlier version said incorrectly that the Ipsos Mori poll published this week was commissioned by the pro-EU Business for New Europe group.