Brexit minister David Davis called on the European Union on Sunday to relax its position that the two sides must first make progress on a divorce settlement before moving on to discussing future relations.
After a slow start to negotiations to unravel more than 40 years of union, Britain is pressing for talks to move beyond the divorce to offer companies some assurance of what to expect after Britain leaves the EU in March 2019.
This week, the government will issue five new papers to outline proposals for future ties, including how to resolve any future disputes without "the direct jurisdiction of the Court of Justice of the European Union (ECJ)", Davis said.
"I firmly believe the early round of the negotiations have already demonstrated that many questions around our withdrawal are inextricably linked to our future relationship," Davis wrote in the Sunday Times newspaper.
"Both sides need to move swiftly on to discussing our future partnership, and we want that to happen after the European Council in October," he wrote, saying the clock was ticking.
EU officials have said there must be "sufficient progress" in the first stage of talks on the rights of expatriates, Britain's border with EU member Ireland and a financial settlement before they can consider a future relationship.
That has frustrated British officials, who say that until there has been discussion of future ties, including a new customs arrangement and some way of resolving any future
disputes, they cannot solve the Irish border issue or financial settlement, two of the more difficult issues in the talks.
"There are financial obligations on both sides that will not be made void by our exit from the EU," Davis wrote. "We are working to determine what these are - and interrogating the basis for the EU's position, line by line, as taxpayers would expect us to do."
He said the Brexit ministry would "advance our thinking further" with the new papers next week.
On the role of the ECJ, Davis said Britain's proposals would be based on "precedents" which do not involve the "direct jurisdiction" of the court, which is hated by many pro-Brexit ministers in the governing Conservative Party.
EU officials say the court should guarantee the rights of EU citizens living or working in Britain after Brexit.
"Ultimately, the key question here is how we fairly consider and solve disputes for both sides," Davis wrote.