Reforming Britain's membership of the EU will not be "mission impossible," David Cameron will say today.

The Prime Minister, who has frustrated some EU officials by giving away few details on the changes he would like to see, will publish a letter sent to the President of the European Council Donald Tusk, setting out his four main objectives.

His demands to Tusk are: guaranteeing of fairness for non euro zone members, greater competitiveness, exemption from the treaty principle of an "ever-closer union" and restricting EU migrants' access to in-work benefits such as tax-credits.

"There will be those who say, here and elsewhere in the EU, that we are embarked on Mission Impossible," Cameron will say in a speech in London, according to advance extracts released by his office. "I do not believe so for a minute."

However eurosceptic campaigners who want Britain to leave the EU have called his requests a "gimmick." The Vote Leave campaign, one of three competing 'out' campaigns, said it expected Cameron to get what he asks for because they are "trivial" demands.

However the issue of restricting migrants' access to in-work benefits is likely to cause tensions among EU leaders who fear it will discriminate against their citizens. This will be the most politically charged of Cameron's four demands.

The British leader has said he favours staying in a reformed EU but he will also use the speech to give his strongest warning yet that he might back Britain leaving the 28-member bloc unless other leaders agree to his demands.

The letter will mark a significant step towards Britain's referendum on EU membership which, if Cameron is to keep his manifesto promise, must take place before the end of 2017. The letter will prompt the start of a renegotiation period before a December summit of EU leaders to hammer out the details of Britain's new terms.

"When you look at the challenges facing European leaders today, the changes that Britain is seeking do not fall in the box marked 'impossible.' They are eminently resolvable, with the requisite political will and political imagination," Cameron will say in his speech ahead of the publication of the letter.

"The European Union has a record of solving intractable problems. It can solve this one. Let us therefore resolve to do so," he will say in the letter.

Cameron has ramped up the case against those wanting to leave the EU in recent weeks, stressing the benefits of being in a reformed organisation, after polls showed a narrowing gap between the "Yes" and "No" camps.

Opinion polls, however, still show that a majority of Britons favour staying within the bloc.

Additional reporting from Reuters.