Sweden's minister for EU affairs and trade, Ann Linde, hit out against the situation as she visited Downing Street last week.
Ms Linde said she was shocked by the xenophobia and uncertainty experienced by around 100,000 Swedes currently living in Britain.
She said: “This is one of the very most important issues and we have to solve it in a very constructive way in the first part of the negotiations."
The European Union minister’s remarks followed a meeting with Swedish citizens, where it was claimed they had experienced a series of xenophobic incidents since last year’s referendum.
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Ann Linde said she was shocked by the xenophobia and uncertainty experienced by Swedes
One woman, who works for a bank, told Ms Linde one of her colleagues had said Britons had voted for “people like her” to leave the country.
Following the incident, the Swede continued, her boss had sent out an e-mail saying that such behaviour would not be tolerated.
Another added they had been offered a contract with a clause which stated that if the employee could not guarantee their right to remain in the country, they could be terminated with immediate effect.
“All but one of them explained they had been subjected to xenophobia,” Ms Linde said.
All but one of them explained they had been subjected to xenophobia
In a meeting with Brexit secretary David Davis and international trade secretary Liam Fox, the leading politician urged Theresa May’s Cabinet to address the issue urgently.
While around 100,000 Swedes have taken up residency in the UK, it is estimated around 30,000 Britons have made the Scandinavian country their home.
The Swedish minister said that, during their meeting, Mr Davis had expressed his “absolute desire that we can find a solution where everyone can stay”.
Meanwhile, Ms Linde added she could not give assurances to British people in Sweden because it was a “wider EU-issue”.
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Continued cooperation with the EU to tackle terrorism and international crime.
She said: “I don’t offer anything. This is part of the EU negotiation that is conducted by the EU commission.
“What I hope is we have a negotiation result where the Swedes who live in Britain can continue to do so and the Brits who stay in Sweden continue to do so.”
Revealing the Government’s Brexit plan last week, Theresa May declared: “I want us to be a secure, prosperous, tolerant country – a magnet for international talent and a home to the pioneers and innovators who will shape the world ahead.
"I want us to be a truly Global Britain – the best friend and neighbour to our European partners, but a country that reaches beyond the borders of Europe too.
"A country that gets out into the world to build relationships with old friends and new allies alike."