After weeks of cross-party talks, the government's negotiating team is expected to present Labour with a formal offer on the key issue of Britain's customs relationship with the European Union after Brexit.
Britain's Prime Minister Theresa May has not managed to get a Brexit deal across the line.
In addition, Prime Minister Theresa May will meet backbench representatives who are reportedly keen to know when she will step down.
May responded by noting that she had agreed a deal with the European Union to leave, but MPs had rejected it three times.
"She's leading us to oblivion - I don't understand why she is hanging on", says one former cabinet minister.
Brady, along with many Conservative MPs, want May to spell out her departure plans in more detail having previously committed to remaining in Downing Street until a Brexit deal is passed.
Two new parties - the anti-EU Brexit Party led by Nigel Farage and the pro-European Change UK party - are campaigning hard, hoping to make gains among disgruntled Britons.
"The prime minister deeply regrets that we haven't left the EU on time. and that a outcome of that is that we will have to take part in the European elections", the spokesman said.
"We need a resolution because there is an existential threat to the Conservative Party".
Flustered Prince Harry thanks the horses after announcing birth of his son
He said: "I'm very excited to announce that Meghan and myself had a baby boy this morning, a very healthy baby boy". Alongside the Duke was wife Kate, who also congratulated Prince Harry and Meghan on the birth of their son.
However, he said that he did not believe a permanent customs union with the EU - supported by Labour - offered a "sustainable, long-term solution" to the current impasse.
Anger within the Tory ranks at Mrs May has been fuelled by the potential for a softer Brexit deal with Labour.
The government and Labour resumed cross-party talks on breaking the Brexit stalemate at 6pm on Wednesday evening.
In the latest round of talks, chancellor Philip Hammond and deputy PM David Lidington are expected to meet Labour's John McDonnell and shadow Brexit secretary Sir Keir Starmer. Like the Conservatives, the Labour Party fears voters will again punish them by voting for alternative parties which have a clearer stance on Brexit.
'And, I would have thought that fairly soon after that would be time for her to think about setting a schedule to find her successor.
He told a meeting of Conservatives last night the deal could be put to a vote in the next few days.
The Tory MP for the Cotswolds said it was the Prime Minister's decision on when she should go but he would "absolutely" support grass roots moves to try to topple her in June if her departure date was not imminent.
However, Labour's business spokeswoman Rebecca Long-Bailey said the government had not offered any new concessions.
The Conservatives will now have to fight in European elections that they did not want to hold, while fighting on both their eurosceptic and europhile flanks.