The country's top court must decide whether Johnson broke the law when he shut down Parliament for five weeks until Oct. 14. He says it was a routine measure, but opponents claim he was trying to stop lawmakers scrutinizing his Brexit plans.
At the end of a three-day hearing, Brenda Hale, president of the Supreme Court, said the court would give its ruling "as soon as it humanly can." She said the 11 judges hoped to rule "early next week."
If the government loses, Johnson could be forced to recall Parliament.
The European Commission says it has received new documents from the British government as discussions resume between the sides to try to find a Brexit compromise.
Spokeswoman Mina Andreeva said Thursday that the commission has "received documents from the UK and on this basis we will have technical discussion today and tomorrow on some aspects of customs, manufactured goods and sanitary and phytosanitary rules."
Andreeva added that European Commission President Jean-Claude Juncker had a phone conversation with British Prime minister Boris Johnson on Wednesday after the pair met in Luxembourg for a working lunch earlier this week.
Andreeva said that Juncker told Johnson that a "deal is desirable and still possible."
In addition to the planned technical discussions, Andreeva added that the EU's Brexit chief negotiator, Michel Barnier, and Britain's chief Brexit minister, Stephen Barclay, will also discuss Brexit on Friday at a "political level."
The British government says it has sent written proposals to the European Union on how to rework the rejected Brexit divorce deal.
The government said Thursday it sent "confidential technical non-papers which reflect the ideas the U.K. has been putting forward." Non-papers are documents intended for discussion, rather than formal proposals.
Although Prime Minister Boris Johnson insists Britain is working hard to get a deal, the EU says it is still waiting to hear concrete ideas.
Britain's statement came after Finland's prime minister said the U.K. needed to submit its proposals by the end of September, or "it's all over."
Britain said it would not meet an "artificial deadline" but would make formal submissions "when we are ready."
The U.K. is due to leave the EU on Oct. 31.
Finland's prime minister is warning Britain it must come up with solid new Brexit proposals by the end of the month or the European Union will not consider them.
Antti Rinne said EU nations were in agreement that alternatives must be provided in writing by Sept. 30.
Finland holds the rotating presidency of the 28-nation bloc. Rinne spoke Wednesday after meeting French President Emmanuel Macron in Paris.
According to Finnish broadcaster YLE, he said: "If the UK wants to discuss alternatives to the existing exit agreement, then these must be presented before the end of the month."
Britain is due to leave the EU on Oct. 31, and Prime Minister Boris Johnson says he is working to strike a deal. EU leaders, however, say Britain hasn't not produced any concrete proposals.
Britain's Supreme Court is set to finish hearing a case that will determine whether Prime Minister Boris Johnson broke the law by suspending Parliament just weeks before the U.K. is due to leave the European Union.
Judges at the country's top court will hear Thursday from a lawyer for former Prime Minister John Major, who is among those challenging the decision by Johnson, one of his successors as Conservative leader.
The government's opponents claim Johnson sent lawmakers home until Oct. 14 to prevent them scrutinizing his plan to take Britain out of the EU at the end of next month, with or without a divorce deal.
The government says the suspension is routine and not motivated by Brexit, and argues that judges should not interfere in politics.