The Conservative vice-chairman Kemi Badenoch has provoked Labour anger after she accused the heavily pregnant opposition MP Tulip Siddiq of “making a point” by insisting on voting in Tuesday evening’s Brexit debate.

Badenoch said she had heard Siddiq “speak on this issue privately before” and that she was choosing to go to Westminster to vote because “she wants to make a point she is doing this for her constituents”.

The Conservative was speaking on the BBC’s Politics Live a day after it emerged that Siddiq had delayed a caesarean section by two days so she could vote against May’s Brexit deal in the Commons.

Badenoch added that it was not necessary for Siddiq to take the trouble to vote, conceding that May’s deal was expected to be heavily defeated and arguing that “one vote isn’t going to make a difference”.

The Conservatives say they have offered Siddiq “a pair”, in which they would ask one of their loyal MPs to abstain so that the Labour MP’s absence would not affect the overall result.

But shortly after Badenoch’s interview, Siddiq tweeted that “my decision to delay my baby’s birth is not one I take lightly”. She added that she had “no faith in the pairing system”.

She said that in July “the Govt stole the vote of new mother”, referring to a previous episode when the Conservative chairman, Brandon Lewis, voted in a crucial Brexit debate despite being paired with the Lib Dem MP Jo Swinson, who was at the time on maternity leave.

Thank you all for supportive messages. My decision to delay my baby's birth is not one I take lightly. Let me be clear, I have no faith in the pairing system - in July the Govt stole the vote of a new mother. It's my duty to represent Hampstead & Kilburn, and I will do just that. — Tulip Siddiq (@TulipSiddiq) January 15, 2019

Other Labour MPs criticised Badenoch’s suggestion that Siddiq’s actions were politically motivated. Louise Haigh demanded that Badenoch make an immediate apology while Diana Johnson said Siddiq was “having to make a point because of the cruel decisions of a male-dominated government whips office”.

Siddiq will travel to Westminster to vote in the Brexit debate with her husband. Her office has arranged with the Commons authorities for her to be picked up in a wheelchair, allowing her to be pushed through the division lobby to ensure her vote is counted.

Tulip Siddiq said she had no faith in the pairing system. Photograph: Yui Mok/PA

It is theoretically possible for Siddiq to be “nodded through” if she simply makes it on to the Westminster estate – a system whereby a member who is physically unable to make it through the Commons division lobbies can have their vote counted.

But it is understood that Siddiq wants to go through the lobby in person, again because she is concerned that the Conservatives will not honour the system.

The Labour backbencher Naz Shah was pushed through the division lobby in a wheelchair while wearing pyjamas last June, at a time when she was recovering from a serious illness because the Conservatives refused to allow her to be nodded through.

On Thursday, John Bercow, the Commons Speaker, said that Siddiq should be allowed to vote by proxy, meaning that her vote be counted in her absence. She would have been the first MP to be allowed to vote in this fashion, but while Conservative sources said a proxy would be offered, this had not taken place.