London (dpa) - British lawmakers will vote on a second set of alternatives to Prime Minister Theresa May's Brexit deal on Monday, as the government appeared to sink further into chaos.

New Brexit date

Britain is currently set to leave the European Union on April 12, but lawmakers have overwhelmingly rejected Conservative premier May's deal three times. They also failed to unite around any alternative in a first round of indicative votes last week.

Poll: More Brits now against Brexit than in favour

The proposals on the table on Monday as part of the non-binding, "indicative" votes include a deal that would keep Britain in the EU's customs union and a referendum on whatever deal is agreed.

Many politicians believe a slim majority is possible for some form of softer Brexit involving a customs union, amid speculation that May could be considering this option.

May's chief whip, or convenor in parliament, Julian Smith, told the BBC that the government "probably should have just been clearer" that losing its majority in a disastrous snap election in June 2017 "would mean that this would be inevitably a kind of softer type of Brexit."

British media reported that hard-line pro-Brexit cabinet ministers have threatened to resign if May backs a customs union agreement, which would prevent Britain from striking bilateral trade deals with other countries.

"This is, I think, the worst example of ill-discipline in cabinet in British political history," Smith said in advance excerpts of a BBC documentary, "The Brexit Storm," scheduled for broadcast on Monday night.

Concerns about Brexit-deal

Leading eurosceptic Jacob Rees-Mogg told London radio station LBC that he is "very concerned" about the possibility of May shifting towards backing a customs union with the EU.

"My concern is that the prime minister is more concerned to avoid a no-deal Brexit than anything else," Rees-Mogg told the broadcaster, adding that he would "continue to campaign to get us out of the customs union" if Britain remained in it.

May is also reportedly attempting to bring her deal before parliament for a fourth time, possibly as early as Tuesday, in the hope that the Conservative eurosceptics will finally support it for fear that parliament will vote for a customs union option.

If Britain wants to avoid leaving the EU without a deal it must request an extension, which must be agreed to by the other 27 EU member states and could force it to take part in May's European Parliament elections.