"The Prime Minister underlined that the negotiations were now in a serious situation. Time was very short and it now looked very likely that an agreement would not be reached unless the EU position changed substantially," said the spokesperson in a statement issued after a phone call between Johnson and European Commission President Ursula von der Leyen Thursday evening, reports Xinhua.
Britain was "making every effort to accommodate reasonable EU requests on the level playing field, but even though the gap had narrowed some fundamental areas remained difficult," said the statement.
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"On fisheries he (Johnson) stressed that the UK could not accept a situation where it was the only sovereign country in the world not to be able to control access to its own waters for an extended period and to be faced with fisheries quotas which hugely disadvantaged its own industry," said the statement.
"The EU's position in this area was simply not reasonable and if there was to be an agreement it needed to shift significantly," it added.
The prime minister repeated that little time was left and "if no agreement could be reached, the UK and the EU would part as friends, with the UK trading with the EU on Australian-style terms," said the statement. Australia trades with the EU largely on the World Trade Organization (WTO) terms.
"The leaders agreed to remain in close contact, said the statement.
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For her part, von der Leyen said on Twitter that the EU "welcomed substantial progress on many issues. However, big differences remain to be bridged, in particular on fisheries. Bridging them will be very challenging."
"Negotiations will continue tomorrow," she said.
Earlier Thursday, British Cabinet Office Minister Michael Gove said the British government "will be doing everything" to secure a good post-Brexit trade deal with the EU.
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However, Gove reaffirmed that Britain would walk away if a trade deal was not "in the best interests of our country".
Also on Thursday, EU's chief Brexit negotiator Michel Barnier noted that "good progress" has been made in the trade negotiations.
"Good progress, but last stumbling blocks remain. We will only sign a deal protecting EU interests and principles," he tweeted after updating European Parliament leaders on the negotiations.
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The British and EU leaders have previously said significant differences remained between the two sides on three critical issues: level playing field, governance and fisheries. The latest reports suggested that fishing rights remains the last major sticking issue between the two sides.
The trade negotiations are at a crucial stage as time is running out for both sides to secure a deal before the Brexit transition period expires at the end of the year.
Failure to reach a free trade agreement means bilateral trade will fall back on WTO rules in 2021.
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