Britain’s biggest banks are preparing to relocate out of the UK in the first few months of 2017 amid growing fears over the impending Brexit negotiations, while smaller banks are making plans to get out before Christmas.

The dramatic claim is made in the Observer by the chief executive of the British Bankers’ Association, Anthony Browne, who warns “the public and political debate at the moment is taking us in the wrong direction”.

A source close to the Brexit secretary, David Davis, said he and the chancellor, Philip Hammond, had last week sought to offer reassurance that they were determined to secure the status of the City of London.

However, the government’s stated intention to take control of the freedom of movement into the UK is widely recognised among officials to be a hammer blow to any chance of retaining the present terms of trade for banks, particularly given the bellicose rhetoric of major politicians on the continent.

The so-called passporting rights for members of the single market allow UK-based banks to offer financial services to companies and individuals across the EU unimpeded, yet the French president, François Hollande, is among those who have insisted in recent weeks that hard Brexit will mean “hard negotiation” and Britain will need to “pay the price” of leaving.

A hard Brexit would involve the UK leaving both the single market, a central pillar of which is freedom of movement, and the customs union, which could potentially reintroduce tariff and non-tariff restrictions on British imports and exports.

Browne warns that British and European politicians who appear to be pursuing “anti-trade” goals need to recognise that “putting up barriers to the trade in financial services across the Channel will make us all worse off”.

Browne, whose organisation has been in intense negotiations with the government, further warns the EU that banks based in the UK are currently lending £1.1tn, therefore “keeping the continent afloat financially”, and this arrangement is at risk.

Anthony Browne of the British Bankers’ Association says the whole of Europe will suffer if the UK chooses a hard Brexit. Photograph: Bloomberg

Of Britain’s position, he writes that banking is the country’s biggest export industry by far and the current trajectory threatens not just tariff-free trade, but the legal right of banks to provide services.

“Most international banks now have project teams working out which operations they need to move to ensure they can continue serving customers, the date by which this must happen, and how best to do it,” he says.

“Their hands are quivering over the relocate button. Many smaller banks plan to start relocations before Christmas; bigger banks are expected to start in the first quarter of next year.”

Sources close to Davis dismissed speculation that he believed a solution would be for the City to strike an “equivalence” deal with the EU, under which the regulatory systems are recognised by both parties through a one-off agreement. Browne writes that some Brexiters have made such an argument, but such a deal would not be enough to stop banks deserting Britain.

“On this side of the Channel, some high-profile Brexiters have poured scorn on the idea that we need passporting at all and that other regimes such as ‘third country equivalence’ will do,” he says.

“But the EU’s equivalence regime is a poor shadow of passporting – it only covers a narrow range of services, can be withdrawn at virtually no notice, and will probably mean the UK will have to accept rules it has no influence over. For most banks, equivalence won’t prevent them from relocating their operations.”

It has been reported that Goldman Sachs is among those drawing up plans to transfer around 2,000 of its employees to a rival European city, should the UK lose its passporting rights.

The industry body TheCityUk has claimed that up to 70,000 financial jobs could be lost if Britain leaves the EU without a new, credible relationship in place for the City of London.

Browne says he understands the motivation of those who are seeking to take business from UK shores, but he condemns politicians who appear to be willing to break up the integrated financial market, which “makes it easier and cheaper for French farmers, German manufacturers and Italian fashion designers to secure funding”.

He writes: “It is understandable that other European cities want to attract jobs from London. Delegations from Frankfurt, Paris, Dublin and Madrid are all coming to the UK to pitch to bankers. I am pro-competition, and long may they try to make their labour market and fiscal policy more attractive to international investors.

“That is not the problem. The problem comes when national governments try to use the EU exit negotiations to build walls across the Channel to split Europe’s integrated financial market in two, in order to force jobs from London.”

The scale of the task facing the UK in striking a good Brexit deal with the EU has been put in stark relief by the apparent collapse of the proposed EU-Canada trade pact.

On Saturday, there were frantic diplomatic efforts to salvage a deal after Canada’s international trade minister, Chrystia Freeland, walked out of talks. She described the situation as “impossible” on Friday and cast doubt on the bloc’s ability to operate effectively after the proposals were blocked by a regional administration in Belgium.

The parliament in Wallonia is holding up the deal, although the region’s leader, Paul Magnette, suggested the standoff could be resolved within days. It has concerns the deal will undermine labour, environment and consumer standards, and allow multinationals to crush local firms.