UK negotiators have told their counterparts in Brussels that about 7,000 European-based investment funds that rely on British clients for their cash and profits will be hit by regulators unless the EU changes its position on the City of London after Brexit.

As frustration grows within Whitehall at what is seen as a dogmatic position taken by the EU’s chief negotiator, Michel Barnier, the British side has upped the ante by making an implicit threat to EU interests.

A section of a UK presentation made to the European commission’s negotiators last week, and seen by the Guardian, says that unless Brussels allows all UK sectors of the City of London to continue to operate after Brexit as they do today, at least initially, obstacles to European financial interests operating in the UK could also be put in place.

The British government says the EU’s “equivalence regime”, under which UK providers would have the right to offer financial services in the European economic area after Brexit, does not cover enough sectors or provide adequate assurances to UK-based banks and fund managers.

The UK also wants equivalence decisions to be made collaboratively between Brussels and Whitehall on whether parts of the financial sector will be able to continue to operate across the Channel as regulations diverge after Brexit.

As it stands, a declaration of equivalencecan be easily revoked with only 30 days’ notice under existing EU legislation.

The EU is resisting, and insists it will not offer a bespoke deal on financial services. It says that what works for US financial services providers will have to work for the UK.

The UK negotiators’ presentation given last Wednesday warned that without fresh thinking both sides would raise damaging barriers to trade. “There is no third country equivalence regime to support the rights of around 7,000 EEA [European Economic Area] domiciled funds to market to UK retail customers, who operate under the passport today”, the paper said.

It is likely the EEA-domiciled funds would be allowed to continue to offer services in the UK, but only having cleared additional regulatory hurdles and on the understanding that they could easily lose their freedom to operate.

British negotiators also complained last week that Barnier had misinterpreted the UK’s position in his reporting back to the member states on the Brexit white paper.

The suggestion that the UK’s proposals would limit the EU’s power over its own rules in relation to the financial sector infuriated Whitehall officials.

The UK’s paper repeatedly stresses the importance of both the UK parliament and EU institutions maintaining their “autonomy of decision-making and the ability to legislate for their own interests”.

A senior EU official responded that Brussels had been “very kind to the white paper, given that it is a completely unworkable document”.

In a sign that the complaint had hit home, however, Barnier appeared to concede to the British point during a joint press conference with the Brexit secretary, Dominic Raab, on Friday.

He told reporters: “We discussed financial services this week and agreed that future market access will be governed by autonomous decisions on both sides.

“We recognised the need for this autonomy, not only at the time of granting equivalence decisions, but also at the time of withdrawing such decisions.

“And we agreed to have close regulatory cooperation, which will also have to respect the autonomy of both parties.”

Should the UK follow the EU’s model and not grant the 7,000 EEA-domiciled funds easy access to the British market, it is likely there would be a three-year buffer to allow them to make necessary changes to their operations under current plans.