"They're not going to go on for months, they're certainly going to continue next week", Lidington said.
He said meetings later this week would be divided into different subjects led by relevant ministers and their Labour opposite numbers.
The letter, seen by the Daily Mail, accuses the Prime Minister of breaking "solemn pledges" to honour the referendum result and "leave the European Union on time on March 29".
Mr Corbett said: 'If Labour does not reconfirm its support for a confirmatory public vote on any Brexit deal in its manifesto it will haemorrhage votes. It will make writing the manifesto impossible'.
Tory grandees have raised the possibility of a change in the rules governing challenges to the party leader.More news: Oculus accidentally ships out thousands of Oculus Touch controllers with creepy messages
She has been unable to persuade MPs to back the withdrawal terms she has struck with Brussels, but is also unwilling to take Britain out of the European Union with no deal at all.
The Brexit Party has 70 candidates and sees the upcoming elections, which begin on May 23, as a "first step", Farage said at the launch event in the English city of Coventry on Friday.
He said: "We really have to get out and we simply can not fight the Euro elections".
If the cross-party talks do not end in an agreement, then Mr Lidington said the Government would "put before Parliament a set of options" which it would "actually having to come to a preferred option" on "rather than voting against everything".
Writing in the Daily Telegraph, he admitted he had been tempted to vote Ukip in the last Euro elections.More news: ‘Titans’ adds ‘Game of Thrones’ actor Iain Glen as Bruce Wayne
Energy minister Claire Perry yesterday said it was still possible that the elections could be cancelled if Parliament passed a Brexit deal after MPs return from their Easter break.
He added: "I am a little bit anxious that the European Union in future will be determining trade deals and we won't really have a say".
The British cabinet office minister who is leading the Brexit talks between the government and the Labour party has said discussions on a compromise deal will continue this week, but they can not be allowed to drag out for too long.
He said the two sides would "take stock" after Easter before deciding whether a deal is possible.
The MP for Chingford and Woodford Green warned against his party embracing Labour's Brexit policy, saying he had "real concerns with some of my colleagues going out lauding Jeremy Corbyn".More news: House committee chair extends deadline for Trump's tax returns