By Stephen Fidler

No industry cluster has better exploited the European Union’s single market than financial institutions in the City of London.

Using so-called passporting rights that allow firms based in one EU country to do business across the bloc, the City has become the overwhelmingly dominant force in European finance.

Now financial institutions based in the U.K. are resigned to losing their passport when the country leaves the bloc, probably in 2019. And the current most likely alternative arrangement would be a poor substitute that bankers say wouldn’t provide a reliable basis for doing business inside the EU.

Passporting will likely disappear because British Prime Minister Theresa May has ruled out the most viable course for retaining it once Britain leaves the EU: moving into the European Economic Area alongside Norway and others.

The alternative, known in the jargon as equivalence, gives financial institutions based in non-EU countries the right to perform some business in the bloc based on an assessment that their regulation and supervision at home is at least as effective as it would be in the EU.

On the face of it, that should work for the U.K. Mrs. May has promised a “Great Repeal Bill” that would enshrine all EU law in U.K. law, an unprecedented step that some Brussels officials have jokingly dubbed the Great Copy-Paste Bill. This would avoid any legal vacuum in the U.K. and mean that, at the moment of Britain’s departure, its financial regulation would be exactly equivalent to the EU’s.

Yet there are several reasons why many banks wouldn’t want to hang their European strategies on the equivalence peg, and why it would be unsatisfactory for the British government too.

The first problem is who gets to decide on equivalence. That power resides with the European Commission, the Brussels bureaucracy whose yoke the British are supposed to be escaping.

The British government “sees equivalence as a very poor substitute for loss of the EU passport, primarily because it will give the European Commission a huge amount of discretionary power in determining whether U.K. laws are indeed equivalent to those in Europe,” said Mujtaba Rahman, Europe head of the Eurasia Group consulting firm.

That would be hard to square, he said, with the narrative that the U.K. is regaining sovereignty by leaving the EU.

The commission has taken years to come to conclusions in the past—for example over U.S. firms that clear derivatives transactions—and can revoke its decisions at any time.

“This framework offers a fairly bleak basis on which the City might continue to thrive as a global financial center in Europe,” wrote Karel Lannoo, chief executive of the Centre for European Policy Studies in a recent paper.

He said equivalence only applies to some activities, mainly in wholesale rather than retail finance, and would furnish only a very limited access to the single market as compared with today.

It would also constrain the U.K.’s ability to adjust financial regulation in the future. If Britain chose to adopt lighter-touch regulation to attract more financial institutions from around the world, it would reduce the prospects of that approach being viewed by the EU as equivalent, he said.

To retain equivalence over time, as the EU changed its regulations, the U.K. would also have to adapt its own rules to stay in line.

For that reason, U.K. officials have indicated that they would like to negotiate a better arrangement than equivalence. In an interview this week with Bloomberg, trade minister Mark Garnier spoke of trying to secure in negotiations with the EU “a special hybrid version…with a better version of equivalence or a different version of passporting.”

There are doubts whether this is achievable. “The EU has no incentive to create a hybrid model for the U.K. that allows it to protect the integrity of its financial-services trade with the EU from the outside,” said Mr. Rahman. “Whatever regime is created will be less beneficial [to the U.K.] than the status quo.”