David Cameron is set to outline his plans for EU reform in writing for the very first time. He claims negotiating Britain's relationship with Brussels is not "mission impossible".

The prime minister will vow to tackle to "abuse" of freedom of movement and place a four-year ban on EU migrants claiming benefits as part of four main objectives he will send in a letter to the President of the European Council Donald Tusk.

Cameron has been criticised by some EU leaders for not outlining the details of his reforms ahead of the UK's planned referendum of their membership by the end of 2017. He hopes the letter to the European Council will pave the way for talks among EU leaders.

Despite previously saying he will fight "vigorously" for Britain to remain in the EU at a speech to the Confederation of British Industry (CBI), Cameron will warn that the country could leave the EU if members aren't prepared to show "political will and imagination" to meet his demands.

Cameron is set to call for curbs on freedom of movement that will allow the UK to tackle migration from the EU. Also on the cards are measures to protect the single market for the UK and other countries that do not use the euro, preventing the UK from forming an "ever closer union" with the rest of the EU. Cameron wants to "write competitiveness into the DNA" of the union.

In a speech, Cameron will say: "I have set out today the changes I want to see, and which Britain needs to see. There will be those who say – here and elsewhere in the EU – that we are embarked on mission impossible. I say: 'Why?' I do not deny that seeking changes which require the agreement of 27 other democracies, all with their own concerns, is a big task. But an impossible one? I do not believe so for a minute."

In the letter to Tusk, Cameron will write: "The European Union has a record of solving intractable problems. It can solve this one. Let us therefore resolve to do so."

The speech arrived after Cameorn's talk at the CBI was interrupted by protesters chanting "CBI, the voice of Brussels". Cameron was quick to dismiss the demonstration, telling the two members of Students for Britain, an offshoot of the Vote Leave campaign: "Come on guys, if you sit down now you can ask me a question rather than making fools of yourself by just standing up and protesting."

Dominic Cummings, campaign director of Vote Leave, said: "David Cameron promised fundamental reform but what he's asking for is trivial - he's given up before he's started. The public wants the end of the supremacy of EU law and to take back control of our economy, our borders, and our democracy. The only way to do this is to vote leave - we won't get it by trusting Cameron."