A last minute addition to the government's Brexit bill could secure hard-won victory for Theresa May this afternoon.

Brexit secretary David Davis this afternoon published a written ministerial statement allowing the Speaker to have the final say on whether a motion can be amended or not – a major sticking point among Remainer rebels seeking a meaningful vote on the final deal.

While it still includes the phrase “neutral motion” – which infuriated former attorney general Dominic Grieve and other backbenchers when it was inserted into his amendment at the last minute last week – Davis' update means it is no longer unamendable.

MPs will vote this afternoon on the EU Withdrawal Bill once again, after the Lords backed the "Grieve II" amendment, defying the government which has argued it would "bind" the hands of the UK's negotiating team.

Numbers are tight, with rebels still annoyed at what they saw as the Prime Minister's backtracking on an agreement last week. One Labour MP told City A.M. he had seen at least two wheelchair-bound colleagues being denied "pairing" or "nodding through" privileges, which would normally avoid the need for sick or pregnant members to vote in person.

He likened it to the 1979 no confidence vote in Margaret Thatcher, saying: "There's a real air of desperation that people are being dissuaded from voting – you have someone who is so pregnant they almost certainly shouldn't be here, and someone who can't walk because they're waiting for a hip replacement. It's not a good sign."

It looks highly likely that Davis' statement may have bought the government some additional support, with MPs on both sides describing it as a victory for their argument.

As the debate began, Remainer and would-be rebel Nicky Morgan tweeted: "I welcome acknowledgement from the government that House of Commons standing orders mean that it is the Speaker who determines whether a motion is expressed in neutral terms – on this basis Parliaments vote is meaningful – and I will support Govt Amendment in lieu."