Britain's shock vote in June to leave the European Union sparked fear among the 800,000 Poles living in Britain, particularly following a spate of xenophobic attacks after the referendum.
Prime Minister Beata Szydlo pledged Poland would be a "constructive partner" in potentially fraught divorce negotiations, but said London had to set out a clear vision when formal talks begin by the end of March.
"We need a good compromise which gives both our countries the best possible options for economic and security cooperation," she wrote in The Daily Telegraph newspaper.
"But the initiative for determining British ambitions and expectations as to the future level of cooperation with the EU has to come from London."
In an article published ahead of talks with Prime Minister Theresa May in Downing Street, Szydlo pressed Britain not to use migrants like her UK-based compatriots as a bargaining chip in the negotiations.
"One thing is certain: millions of UK citizens living across the EU, and millions of EU-27 citizens living in the United Kingdom, should not be made to feel like hostages," she wrote.
"That means we have to guarantee... their right of residence."
Szydlo and her defence, interior, finance and foreign ministers attended an inaugural British-Polish summit on Monday, which included a reception for members of the Polish community in Britain.
They discussed a range of issues, including the deployment of 150 British soldiers to northeastern Poland, and Russian action in Ukraine and Syria.
In a joint press conference afterwards, Szydlo said she understood why May could not guarantee the rights of Europeans living in Britain until similar assurances were extended to Britons across the EU.
While stressing that the issue was a priority for Poland after Brexit, she said: "Of course, these guarantees would need to be reciprocal."
With Poles representing one of the largest minority groups in the UK, Poland has taken a cautious approach to Brexit and last week President Andrzej Duda urged politicians to tone down their rhetoric.
"I propose a glass of cold water to cool emotions, so that in the end it doesn't turn out that we all lose -- both the EU and the UK," Duda told Bloomberg.
Both May and Szydlo stressed their warm relations during Monday's summit.
"I firmly believe that if we all approach Brexit in the same constructive and positive manner, then we can secure the right outcome for the United Kingdom and for our European neighbours too," May said.
Poland's foreign and interior ministers flew to London in September following the murder of a Polish factory worker in Harlow, northeast of London.
The June 23 referendum on EU membership was followed by a spike in the number of attacks against foreigners and two Polish police officers were deployed in Harlow following their compatriot's murder.