Theresa May is expected to meet Jeremy Corbyn later after she said she wanted to work with the Labour leader to break the Brexit deadlock.
The prime minister hopes the two of them can come up with a modified version of her deal with the EU that can secure the backing of MPs.
Mr. Corbyn says he wants a customs union and workers' rights to be priorities.
But Tory Brexiteer Boris Johnson has accused Mrs. May of "entrusting the final handling of Brexit to Labour".
Jacob Rees-Mogg, another prominent Brexiteer, described the offer as "deeply unsatisfactory" and accused Mrs. May of planning to collaborate with "a known Marxist".
Mrs. May announced her plan to meet Mr. Corbyn - as well as her intention to ask the EU for an extension to the Brexit deadline - after more than seven hours of talks with her cabinet on Tuesday.
BBC political editor Laura Kuenssberg says the latest move means the prime minister is likely to adopt a closer relationship with the EU - a softer Brexit - than she has agreed so far.
Mr. Corbyn said he was "very happy" to meet Mrs. May and recognized his own "responsibility" to try to break the deadlock.
But the meeting is not expected to take place before this afternoon, at the earliest, says our political editor, who was told by Mr. Corbyn's team that he was not available on Wednesday morning for talks with the PM.