David Cameron provoked a furious backlash by Conservative Eurosceptics last night after he beat a retreat over his opposition to the agreement to enforce budgetary discipline in the eurozone.

Tory MPs who hailed him as a hero last month when he vetoed an EU-wide treaty to save the euro turned their fire on the Prime Minister after he watered down his objections to the "fiscal compact". His critics claimed the gains he made last month had now been lost. At the time, Mr Cameron insisted the other 26 EU nations could not use bodies such as the European Court of Justice (ECJ) to enforce fines on euro members who breach deficit limits. He feared this could harm British industry by eroding the single market.

But at another EU summit in Brussels last night, Mr Cameron nodded through the agreement – although Britain will remain outside it. He told fellow EU leaders there were still legal doubts and that the UK reserved its right to take legal action to prevent the ECJ policing the euro deal. But there is little prospect that the UK will go to law – not least because it would have to take action in the ECJ itself, which normally rules in favour of European integration.

Mr Cameron faces criticism over his retreat when he makes a Commons statement about the summit today. Philip Davies, a Eurosceptic, warned that the new stance would make the Prime Minister look more like John Major than Margaret Thatcher. "We saw in the opinion polls how popular he was in December. He would be equally unpopular if the British public thought he was going to backslide from that position," he said.

Douglas Carswell, another Tory Europhobe, said: "I don't see how the veto is really a veto if we allow the fiscal union to form, and then find ourselves subject to the EU institutions being used to govern that. In effect we will find that for all the talk of a veto, we find ourselves hauled into this process."

The other EU countries vowed to ensure their separate agreement is incorporated into the EU's treaties "within five years". The Prime Minister will face further pressure to sign up to it in about two years.

Mr Cameron tried to use yesterday's gathering to build bridges. But there was little sign of a rapprochement with France as Downing Street hit back at a claim by Nicolas Sarkozy, the French President, who declared in a TV interview on Sunday: "The UK has no industry any more." A British official replied: "What he said is not true." He pointed to figures showing that industrial production as a share of GDP was 15 per cent in the UK and only 12.5 per cent in France in 2009.

There were also tensions between the UK and Germany. A British official cast doubt on the German-driven plan to prevent a repeat of the eurozone debt crisis. "To write into law a Germanic view of how one should run an economy and that essentially makes Keynesianism illegal is not something we would do," the official said.

However, Germany backed down over a plan to force Greece to hand control of its tax and spending decisions to an EU "budget commissioner". Decisions on Greece were delayed until next month. But the eurozone crisis overshadowed an attempt by the EU leaders to unite around a "jobs and growth" agenda.