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British finance firms diluted their bid to retain unfettered access to the European Union after Brexit, accepting that Prime Minister Theresa May's government is unwilling to fight their corner against EU resistance.

In a two-page summary of industry priorities for the upcoming negotiations released on Thursday, TheCityUK lobby group made no mention of its once key demand to safeguard so-called passporting, which allows banks with bases in London to service customers throughout the EU. The banks are now pushing for "mutual access" and additional time to adapt to the new regime.

The banks' climb-down comes after May's government made it clear the finance industry wouldn't get any special status in the divorce talks.

EU representatives and member governments have said they won't accept passporting without May remaining in the single market and accepting free movement of people.

Bankers are now lobbying to win access via so-called regulatory equivalence, formerly their least favorite method of servicing their EU clients.

"The U.K. and the European Union should conclude a bespoke agreement that delivers mutual market access, transitional arrangements to allow for enough time to implement the new relationship and access to talent," TheCityUK said in its report.

"It is in the economic interests of the U.K. and the EU to continue to provide and have access to the widest possible range of financial and related professional products."

In the months since June's referendum, bank executives have privately conceded there is little hope of safeguarding their easy access to the trading bloc after Brexit, despite the importance of finance to the U.K. economy. Trade Minister Mark Garnier said as far back as October that banks would most likely lose their passporting rights.

Access to the EU market through equivalence was previously questioned by some in finance because it doesn't relate to all banking activities, can be unilaterally withdrawn by the EU at any time, and is largely untested. Banks don't see equivalence as a permanent solution, Citigroup Inc. analysts wrote in a research note Wednesday.

The U.K. financial regulator said last September that 5,500 U.K.-registered companies rely on passports to do business in other EU countries, with more than 8,000 European firms accessing Britain in a similar way.

If the U.K. lost all passporting rights, 35,000 industry jobs could be at risk, along with 20 billion pounds ($24.6 billion) of annual revenue and 5 billion pounds in lost tax receipts, according to an Oliver Wyman report published in October.

The impact on the wider financial ecosystem of such an outcome could "almost double the effect of Brexit," the report said.

To avoid the need for preemptive staff moves outside Britain, the banks want an interim agreement soon after May triggers the Article 50 exit clause, which she plans for March.

Such a deal would guarantee temporary access to the EU single market beyond the end of the two-year Brexit negotiation period, in case trade barriers are erected at the end of that process if no deal is reached.

That would ensure the status quo would hold until a lasting deal on financial services is struck between the U.K. and the EU.

While the prime minister has previously said she wants the best possible deal for banks, last week she indicated that regaining control of immigration was a priority, sending the pound plunging on speculation she's prepared to depart the EU's single market.

"Many customers benefit from the industry's current unfettered access to the EU single market," TheCityUK said. "While respecting sovereignty and immigration control as prerequisites, the U.K.'s exit from the EU should aim to maximize access to EU markets for the products and services offered by providers in the U.K. to EU customers and vice versa."

The lobby group also called on May to "urgently" clarify the status of EU citizens already living and working in the U.K. Future immigration policy should be designed to make it easier for banks to hire employees from all over the world, especially for specialist jobs, the report said.