The case for staying in the EU will be easier to make by a newly strengthened PM who has already appealed successfully to economic competence

As the City of London celebrates a Conservative victory, it must also face a referendum on the UK’s membership of the European Union. That poll must happen by the end of 2017 if David Cameron is to honour the Tories’ manifesto commitment. The prospect will now dominate debate in the business world until polling day.

Not every business leader wants the UK to stay in the EU, but it is reasonably clear that most do. In the City and financial establishment, opinion is even more one-sided in favour of membership. Expect to see a full-throttle lobbying campaign, accompanied by dire warnings that investment in the UK is at risk and that the City’s status as a global financial centre is under threat. It will make business lobbying for a no vote in the Scottish referendum look like a tea party.

Indeed, some City economists argued in recent weeks that the EU issue was so important that another Tory-led coalition government might have been the “best” outcome for the UK economy. “Given the potential adverse effect on the UK economy of Brexit risk, in our view a minority Conservative-led government [that is unable to pass an EU referendum bill] might be less risky for the UK economy than a Conservative-led majority that can pass a referendum bill,” argued Citigroup.

Possibly. In practice, one suspects Cameron’s stunning general election victory strengthens his hand in keeping the UK in the EU – which one assumes will be the position he eventually adopts.

First, his personal authority is strengthened, so he ought to be less vulnerable to attacks from the Eurosceptic wing of the Conservative party. Second, one clear message from the election is that the Tories’ appeal to economic competence was heard. The pro-EU lobby starts with a huge advantage if it can equate economic stability with membership. Third, while one in eight votes backed Ukip, the party may not be led by charismatic Nigel Farage, previously assumed to be its best electoral asset. Fourth, the SNP – the other big winner last night – is a pro-EU party.

According to Cameron’s script for the referendum, he must first conduct a tour of European capitals to renegotiate the UK’s relationship with the EU. This adventure could yield nothing, it is true. But other EU leaders must now accept that a UK referendum is a reality, not a vague possibility, which changes the rules of engagement.

A full EU treaty change feels highly unlikely, but one suspects Cameron will be able to pluck a few concessions from the negotiations – on immigration rules or voting rights – and present them to UK voters as a triumph of negotiation, even if the boast is thin. It worked for Harold Wilson in the 1975 referendum. And if Greece were to exit the euro, Cameron’s chances might be boosted further: the great European project will be in terrible shape if the euro has lost a member and the EU itself is in danger of losing its second-largest economy.

There are, of course, two differences from 1975. Ukip exists and the press is more Eurosceptic. But it is safe to assume that the frontbenches of all three major parliamentary parties – Tories, Labour and SNP – will be arguing for continued membership. The Eurosceptics on the Tory backbenches can make life awkward for Cameron but he still holds the strongest card – the appeal to economic stability.