Ed Miliband is facing a backbench revolt over immigration policy as senior Labour MPs publicly warn of catastrophic consequences for the party unless he seeks constraints on the free movement of EU workers.

The unrestricted entry of EU citizens from eastern Europe since 2004 is hurting the "very communities that the Labour party was founded to represent", the MPs claim in an open letter published in the Observer.

Miliband is urged by the rebels, including two former ministers, to commit a Labour government to seeking to constrain the free movement of labour from European countries with much lower incomes than the UK, such as Romania and Bulgaria. Two million national insurance numbers have been issued to nationals from eastern European accession countries since 2004.

In an attempt to force Miliband's hand, the MPs claim that the "political consequences of these trends could prove catastrophic for our party unless voters can see we are intent on taking serious action". The MPs' public show of frustration follows a speech by Miliband in Thurrock, Essex, last week in which he reached out to Ukip voters by claiming to understand their concerns while signalling that he would not be offering false promises of radical changes to migration policy in the EU.

The seven rebel MPs, who include Frank Field, Kate Hoey and John Mann, expect to attract further support within the parliamentary party over the coming weeks. They claim that the party's position as it stands is not radical enough.

John Prescott also sided with those wanting significant change to Britain's relationship with the EU. Calling for "radical reform", the former deputy prime minister wrote in his Sunday Mirror column: "One of the key reforms should be a review and reform of the 'freedom of movement' to 'fair movement'," stating that any labour market needs "rules not complete freedom".

In the recent local and European parliament elections, Labour gained 300 councillors and boosted its number of MEPs, but saw Ukip thwart its progress in key target areas, make gains in traditional party heartlands and top the European poll. It was the first time in more than 100 years that neither Labour nor the Conservatives has come top of a national poll.

Miliband and his team were criticised by some party figures for failing to address the concerns of traditional Labour voters tempted by Ukip's anti-immigration message. The Labour MPs, who represent constituencies from across Britain, claim that "concern with immigration has become an increasingly important priority for a large proportion of working- and middle-class voters".

In one section of the letter they write: "Whilst the benefits of mass migration have been served in abundance to many wealthy people, who are in a position to take advantage of cheap labour, we believe that the lack of affordable housing, school places, hospital capacity and transport infrastructure to accommodate this influx of people means that poorer people's living standards have been squeezed."

Since 2004, an average of 79,000 citizens from the new eastern European EU member states have come to the UK each year, while 32,000 a year have left. The population of citizens from the states that joined the EU in 2004, including Poland, is now around one million. Since 2008, the immigrant population from the latest states to join, Romania and Bulgaria, has also steadily risen, to around 150,000.

"As things now stand," the MPs write, "there is nothing to suggest that we won't face large numbers coming to settle here over the next decade."

Sources close to Miliband said they believed the goal of limiting EU migration from countries with relatively low GDPs was unachievable. But the shadow business secretary, Chuka Ummuna, admitted to a conference held by the Blairite Progress campaign group that Britons would be "watching carefully" to see how Labour responds to the polls.

He said: "Ukip topped the poll in the European elections. I don't like that, but that is what happened and we must respect the result. But the British people will now watch carefully how we respond and what we say and do before deciding whether and how to vote next year. I say 'whether' because two-thirds of them did not turn out to vote this time. It is our duty as democrats to do all we can to get people voting."

The rebellion comes as the shadow foreign secretary, Douglas Alexander, privately laid out for the first time Labour's plans on reforming the EU in an attempt to provoke the prime minister into spelling out the Conservative party's aims.

In a letter to David Cameron, Alexander says Labour has five key objectives in future reform negotiations with the other 27 member states: the appointment of an EU commissioner to promote job creation; the ability for states to extend the possible time limits on people coming to work in the UK from countries newly joining the EU; action to stop child benefit and child tax credit being sent abroad to children not living in the UK; a review of the EU budget to help secure further savings and efficiencies, including introducing a need for all EU agencies to newly justify their existence; and the ability for national parliaments to have a greater say in EU policymaking by introducing a mechanism to block unwanted EU legislation.

Alexander writes: "In last week's elections, people across Europe expressed a desire and appetite for change. It is clear that the EU does now face a significant 'reform moment'. Those elections demonstrated a growing lack of trust in politics which will only be reinforced by your failure to let the British people know how you intend to turn your abstract ideas into a real reform programme."

Labour believes Cameron is delaying spelling out his reforms because many of them, including constraining the free movement of workers, are unachievable and will be shown to be so swiftly. A source close to Miliband said: "The Tories are heading for a meltdown on this issue and Cameron needs to come clean sooner rather than later.

"If he is proposing big treaty changes, Europe will laugh him out of court."