Russia is among 20 countries that are looking to squeeze a commercial advantage from Brexit after blocking an attempt by the international trade secretary, Liam Fox, to fast-track a World Trade Organization deal on the UK’s terms of trade with the world.

Whitehall is now facing “up to two dozen” different negotiations with countries over how much meat and dairy produce will be permitted into the British market and what tariffs the UK will set on imports.

The development will pile pressure on the UK’s already strained resources. The Department for International Trade spent more than £1m on recruitment consultants alone in its first year trying to take on experienced trade negotiators, an area that had previously been left entirely to the EU.

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The UK is a full member of the WTO, but as an EU member state it currently shares a set of so-called schedules with the other 27 countries that make up the bloc. Fox, a passionate believer in Brexit, had sought to rush through a set of the UK’s independent schedules on the tariffs and quotas that would be imposed on goods from the world’s major agricultural exporters.

The plan had been for the UK and EU, as independent WTO members, to divide the current quotas between the two according to the historical flows of trade in each product, in what was described as a “technical rectification”.

A large number of countries opposed the plan, however, claiming that they would lose out from the arrangement. The UK will now have to open talks with all those who have opposed the proposals or face trade disputes that could stymie future bilateral trade deals.

David Henig, UK director of the European Centre for International Political Economy, said: “This is ‘Brexit meets reality’, more than a huge problem. It is not a terrific surprise that this has happened. We expected almost all the big agricultural economies – the US, New Zealand – to do this. But in terms of the bilateral free trade deals that we hope to get with Australia, New Zealand and the US, these could be delayed while we haggle over the numbers.

“It’s a complicated discussion and it could easily take a couple of years to sort out and that means it would be three or four years before we could implement bilaterals, so it is likely to introduce delays.”

Despite the setback, the UK will be able to trade on the provisional set of schedules it has tabled while it negotiates with those who withheld support. The tabling of the disputed schedules will also allow the UK government to liberalise their tariffs and quotes on some products to allow non-EU importers to compete with European importers to the benefit of British consumers in the event of a no-deal Brexit.

The UK lodged a 719-page draft of the terms of post-Brexit trade with the WTO earlier this summer, with formal “reservations” raised during a three-month consultation period that has just ended.

Fox told the Commons in a written statement on Thursday: “As expected, some trading partners have expressed reservations about our proposed treatment of tariff rate quotas.”

The Department for International Trade said: “The large majority of our trading partners do not have any objections to our proposed goods schedule. A small number have submitted their concerns and would like to discuss further.

“This was expected and does not impact our ability to trade independently. The terms we have set out will form the basis of our trade policy while we engage with our WTO partners to address their concerns.”