Lidington said the government still hoped Britain would leave the bloc before the new European Parliament takes up its seats in early July.
British Labour leader Jeremy Corbyn will urge both pro-EU voters and Brexit supporters on Thursday (9 May) to vote for his opposition party at this month's European election, a poll he blamed on the Conservative government's "complete failure" to steer the country out of the bloc.
Theresa May has indicated she could bring the Brexit legislation - the Withdrawal Agreement Bill - to the Commons for a vote before MPs break for another recess on the day of the election. But Brexit is on hold amid political deadlock, and so Britons will vote May 23 for lawmakers to fill 73 United Kingdom seats in the 751-seat European Union legislature.
The government has for several weeks been in talks with the main opposition Labour party to find a compromise deal, but there is no sign of progress yet.
Talks between Labour and the Tories aimed at reaching a Brexit agreement will resume on Monday but little concrete progress appears to have been made.
The EU agreed to delay Brexit to allow British politicians to try to agree a way to leave that minimises the impact of the split.
Prime Minister Theresa May's hopes of people in Britain avoiding having to vote in the European Parliament elections were dashed on Tuesday.
In what will be his first visit to Medway as leader, he will make a keynote speech to party activists and members after mixed fortunes in the council elections and continuing uncertainty over Brexit.
Under consideration are a number of methods to get the UK's exit done and dusted, including allowing MPs to rank the alternative Brexit outcomes in order of preference.
Brady said there was no "public clarity" about the timetable for May's departure. "If it were an issue about me and the way I vote, we would already have left the European Union". The parties had agreed on a withdrawal deal, but United Kingdom lawmakers refused to pass it with the Irish backstop being one of the main points of concern for MPs.
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