David Cameron is under mounting pressure to pledge a referendum on UK membership of the EU after overturning decades of British foreign policy by backing full fiscal union for the 17-nation eurozone.

Tory and Labour MPs believe that if the eurozone moves towards a single tax system – as chancellor George Osborne advocated again – then the EU will become a fundamentally different organisation to the one the UK joined in 1973. Many also fear that Britain will come under intense pressure to adapt its tax and regulatory policies to conform more closely with the eurozone once fiscal union is under way, even if the UK remains out of the single currency.

Steve Baker, the Tory MP for Wycombe and a member of the fiercely eurosceptic 2010 Conservative intake, said: "It is very clear that the EU is heading at full speed towards being one country. As that is the case there is absolutely no doubt that the British people should be offered a vote on whether to be a part of that."

Like other Tory and Labour MPs, Baker has signed up to an In/Out referendum being championed by fellow Conservative Zac Goldsmith, the MP for Richmond Park & North Kingston. The campaign will redouble its efforts during the party conference season.

The Observer has also learned that the European scrutiny committee, a select committee of the House of Commons, is to conduct its own inquiries into the effect that fiscal union for the eurozone would have on the UK's economic independence. Its chairman, the veteran Tory MP Bill Cash, said: "Allowing the other member states to go ahead towards fiscal union is a disaster. We must have a referendum in the light of such a profound change in our political relationship with Europe."

For decades the Foreign Office and Treasury have resisted –and said the UK would veto – any moves towards a "two-speed" or "multi-speed" Europe, believing it would lead to pressure on those outside the central core to cede more sovereignty over time. But with the eurozone in crisis, Osborne and Cameron have abandoned that resistance and now believe the euro's only hope of survival is if the EU backs more co-ordination of tax and spending policies. Osborne told Radio 4's Today show: "I think we have to accept that is going to happen. It is in our interest that it happens because an unstable euro is very bad news for us."

The German chancellor, Angela Merkel, and the French president, Nicolas Sarkozy, will meet in Paris on Tuesday to discuss how to beef up "economic governance" across the 17-member single currency zone, amid rising fears about the euro's future.

Jean-Claude Trichet, the outgoing boss of the Frankfurt-based European Central Bank, has called for a euro-wide finance ministry as the only way to prevent a recurrence of the debt crisis which has seen Greece, Portugal and Ireland receive emergency aid.

The ECB was forced to rescue Italy and Spain last week by buying up their bonds, after interest rates for the two countries hit record highs. But it has demanded radical economic reforms and a fresh wave of austerity measures in return. Italian prime minister Silvio Berlusconi announced a controversial package of tax rises and spending cuts.

As the crisis deepened, Bank of England governor Sir Mervyn King made clear at his quarterly inflation report last Wednesday that events in the eurozone posed the greatest threat to Britain's economy, and called for Europe's politicians to get a grip on the situation. "The ECB has gone to the outer limit of what a central bank can do," King said. "Any further action has to be carried out by governments themselves."

One radical solution – backed by Osborne – is to issue "eurobonds", with all 17 countries sharing the responsibility for paying them back. This idea is highly controversial in Germany, where voters fear they would be left paying the bill.

Merkel would be likely to demand tight control over the tax and spending policies of weaker members as a quid pro quo, and France has long favoured more economic co-ordination, but analysts say this "fiscal integration" would fundamentally change the nature of the EU. That could make it harder for Britain to sit outside the eurozone but continue to drive European policy in other areas.

"George Osborne and David Cameron are taking another political gamble, as they did with the cuts," said Olaf Cramme, of the Policy Network thinktank. He believes further fiscal integration among euro members could alter decision-making across the whole EU. "The big difference now is that the euro has become the overriding interest – everything else will be subject to the euro."

Issuing eurobonds could also require a change in the EU's founding treaty, which would have to be approved by all members, including the UK. Many Tory backbenchers hope that would provide an opportunity for renegotiating our relationship with Brussels.