The European migration and refugee crisis could push the UK towards the exit door of the European Union, David Cameron has warned.

The Prime Minister said that in the short term headlines about an influx of refugees, as well as the bloc’s economic problems, could cause people to “push Europe away”.

In an interview with the Spectator magazine he however said he hoped that in the longer-term the British public might take a view that reforming Britain’s relationship with the EU – his party’s policy – was a better approach than leaving.

“I think with both the eurozone crisis and the migration crisis, the short term impact is for people to think, ‘oh Christ, push Europe away from me, it’s bringing me problems’,” he told the magazine.

“I think the longer-term reaction might actually be, 'well if they are going to have a single currency and they are on our doorstep and they are going to try and make it work, let’s make sure our relationship with them works and then we have safeguards, not least for our vital financial services industry so that the system doesn’t work against us'.”

“The short term reaction can be 'get me out of here', the longer term reaction is 'we must find a better way of working with our partners because we share the same challenges'.”

The procession of people arriving in the EU from war-torn and impoverished nations shows no sign of letting up, with the European Commission estimating last month that another three million refugees could arrive before the end of 2016.

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The warning that short-term public opinion could become more eurosceptic because of the migration influx and eurozone’s economic problems comes despite reports that Mr Cameron may seek to hold his promised in-out referendum ahead of schedule.

The Conservative manifesto had promised to hold a vote on membership before the end of 2017, but observers currently estimate that the plebiscite could come as soon as the summer of 2016.

Mr Cameron supports Britain remaining in the EU subject to changes to its freedom of movement and welfare rules.

He last month said he would not rule out Britain leaving the EU if his membership renegotiation demands were not met. He has also said the EU would do "OK" outside the bloc.

There has been little public progress so far on achieving the demands, however, some of which are thought to require renegotiation of the EU’s fundamental treaties and thus the assent of all the bloc’s member state governments – many of whom have expressed public hostility to Mr Cameron’s ideas.

The PM set out four specific demands in November: protection of the single market for non-EU countries, cuts to red tape, exemption for the UK from the bloc’s constitutional drive to “ever-closer union”, and restriction to in-work migrant benefits such as tax credits.