Curbs on the rights of migrants from the European Union to claim state benefits in Britain will be rushed in as David Cameron tries to defuse a growing rebellion by Eurosceptic Conservative MPs.

The Prime Minister will announce today that a rule forcing EU citizens to wait three months before being able to claim jobless benefits will take effect on 1 January.

Regulations will be rushed through Parliament so Romanians and Bulgarians who exercise their new right to come to the UK to work from that date will not be able to draw such payments immediately.

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Mr Cameron announced his intention to impose a three-month wait last month, but Downing Street said at the time the clampdown would not be imposed until an unspecified date next year. That angered rebel Tory MPs, more than 70 of whom are demanding the UK defy the EU by delaying the introduction of the “right to work” for Romanians and Bulgarians.

The MPs will press ahead with a Commons debate on the issue tomorrow. But the passage of the Immigration Bill has been delayed until the new year to lift the threat of an embarrassing defeat for Mr Cameron before 1 January.

He said last night: “The hard-working British public are rightly concerned that migrants do not come here to exploit our public services and our benefits system.

“As part of our long-term plan for the economy, we are taking direct action to fix the welfare and immigration systems so we end the ‘something for nothing culture’ and deliver for people who play by the rules.”

He added: “Accelerating the start of these new restrictions will make the UK a less attractive place for EU migrants who want to come here and try to live off the state. I want to send the clear message that whilst Britain is very much open for business, we will not welcome people who don’t want to contribute.”

The Prime Minister has already announced other measures that will take effect on 1 January. They include cutting off benefits after six months for EU jobseekers with no job prospects, halting housing benefit claims and imposing a 12-month re-entry ban for people who have been removed.

Labour criticised Mr Cameron for not introducing the benefit delay when it proposed the move nine months ago.

Yvette Cooper, the shadow Home Secretary, said: “Why is the Government leaving everything until the last minute and operating in such a chaotic way? Three weeks ago Theresa May told Parliament she couldn’t restrict benefits in time. Now the Prime Minister says they can. They wouldn’t be on the run from angry Conservative backbenchers if they’d listened to us nine months ago.”