The fresh round of the negotiations between Downing Street representatives and the opposition, aimed at passing the withdrawal deal through parliament, began Tuesday and continued on Wednesday.
"After the second day of talks this week, the negotiating teams are working to establish a scope for agreement, and will meet again at the beginning of next week", the Labour spokesperson said as quoted by The Guardian late on Wednesday.
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Meanwhile, the outlet quoted the Downing Street spokesperson as saying that the second round of talks demonstrated the seriousness of both sides in approaching the negotiations.
Graham Brady, the chair of the 1922 Committee, the Conservative Party group in Commons that oversees party leadership, said that May had also agreed to hold a meeting with him next week, in the wake of calls from lawmakers for May to resign amid Brexit uncertainty.
Earlier this week, UK Cabinet Office Minister David Lidington confirmed that the United Kingdom would be unable to ratify the Brexit deal in the next two weeks, and would organize European Parliamentary elections on 23 May, despite hopes to push through a Brexit agreement before this date.
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The United Kingdom was initially supposed to leave the European Union on 29 March. The parties had agreed on a withdrawal deal, but UK lawmakers refused to pass it with the Irish backstop being one of the main points of concern for MPs. The Brexit deadline was subsequently moved to 31 October, with London obliged to participate in EU parliamentary elections if a deal was not passed by 23 May.