Britain has received demands to roll back its human rights standards in exchange for progress on post-Brexit trade deals, including from some countries that ministers are pushing to secure agreements with.

In an admission that some countries have sought to extract a high price for their continuing to trade with Britain after leaving the EU, Liam Fox, the international trade secretary, said some nations had made the requests as part of talks.

Fox said that he would not drop Europe’s standards on human rights in exchange for trade deals, as he explained why limited progress had been made with some nations that the UK currently trades with under EU arrangements.

“Some countries have said that they didn’t like, for example, the human rights elements that were incorporated by the EU and they would like us to drop those in order to roll the agreements over,” Fox said while answering questions in parliament on his department’s progress towards striking trade deals.

“I’m not inclined to do so. The value we attach to human rights is an important part of who we are as a country,” he said.

Although ruling out making changes to Britain’s human rights standards, the detail of the requests could indicate the UK’s weaker bargaining position after Brexit in talks to strike trade deals around the world.

It emerged last week that Japan is seeking tougher concessions from Britain in trade talks than it secured from the EU, with its trade negotiators confident they can extract better terms.

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Ken Clarke, the veteran Conservative MP and supporter of remaining in the EU, told Fox in parliament: “The principle problem is the lack of bargaining power that the United Kingdom on its own has compared with the European Union as a bloc carrying out bargained arrangements.

“Countries like Japan and South Korea and others are going to expect better terms from the United Kingdom, at the expense of the United Kingdom, than they’ve had to give to the EU,” he said.

Fox denied that Britain was in a weaker bargaining position, while arguing that many countries wanted to negotiate trade deals with the UK without the bureaucracy of all EU states having to ratify an agreement.

“We remain the world’s fifth biggest economy and many countries have said to us it would be much easier to do an agreement with the United Kingdom as a single country, that would then negotiate and then ratify, than to have to do it with 28 countries – as they have to do at the present time,” he said.