A Nissan spokesperson said: “We urge UK and EU negotiators to work together for an orderly and balanced Brexit that will continue to encourage mutually beneficial trade.”
Both companies have factories in Derbyshire and Sunderland.
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Nissan’s Sunderland plant received special attention as it supplies nearly 7,000 employees in the region.
However, the company has warned that the plant may not be sustainable if new tariffs are applied to vehicles.
COO Ashwani Gupta told the BBC the company may need to reconsider its future if additional tariffs are imposed.
He added: “You know we are the number one car maker in the UK and we want to keep going. We are determined.
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“Having said that, if we don’t get the current rates, that’s not our intention, but the business will not be sustainable.
“That’s what everyone needs to understand.”
In his letter, Lord Frost raises the question of the rule of origin of goods.
The threshold for parts is leveled at 55 percent, which means that the majority of what has been used must come from the country from which it is exported.
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In his letter, Lord Frost said: “I am sorry to say that so far EU negotiators have not been willing to discuss this or share any proposed text with us.
“The Commission has made it clear that it will not accept cumulation with third countries under any circumstances, which we regret, but which we obviously cannot insist on. ”
The last round of formal Brexit negotiations concluded last week between Michel Barnier and Lord Frost.
Boris Johnson and European Commission President Ursula von der Leyen also held talks on Saturday to discuss the progress of negotiations.
Mr Johnson has set the EU summit for October 15 as the deadline for a deal.
Mainland officials have indicated the end of the month as a more plausible period.
After the talks last week, Barnier met with German Chancellor Angela Merkel to discuss the issues.
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German Foreign Minister Heiko Mass also attended the meeting and warned the UK against a no-deal Brexit.
He said: “Our door remains open for a close and ambitious partnership with Great Britain.
“This is and will remain our goal.”