Reform MPs Lee Anderson, Danny Kruger, Sarah Pochin, Andrew Rosindell and Richard Tice voted against the Universal Credit (Removal of Two Child Limit) Bill at second reading on Tuesday.
Nigel Farage had no vote recorded, according to Parliament’s voting data, but has previously pledged to abolish the limit.
However, Ms Braverman and Mr Jenrick are listed as having voted for the two-child benefit cap to be scrapped.
According to reports, Ms Braverman and Mr Jenrick “got trapped as the doors were locked” after mistakenly entering the aye lobby.
The draft law was supported overall by MPs, passing by 458 to 104 votes, majority 354.
The division took around 20 minutes to complete, with Deputy Speaker Caroline Nokes asking for a delay in the aye lobby to be investigated.
Read more: Two-child benefits cap closer to being scrapped as MPs vote to ditch policy
It comes after Reform’s own policy to lift the cap only for families where both parents are British and in full-time work was branded “racist”.
Party leader Mr Farage had previously pledged to abolish the limit as part of a series of spending promises set out in May last year.
Reform had tabled an amendment to the Bill to halt its progress because it “removes the two-child benefit cap without imposing any other restrictions”.
At a press conference on Tuesday, Mr Farage pledged to halve VAT to 10% for hospitality firms and introduce “staggered” abolition of business rates for pubs over four years.
He said this would be funded through a package of measures, including reinstating the two-child limit for everyone except “British working families”.
Asked whether he thought it was the right look for Reform to be stopping poor households from getting additional benefit income in order to cut the price of a pint, the party leader said: “You could argue it’s not just to cut the price of a pint.
“It’s actually to revivify private enterprise and then get more people back into work, whether it’s part-time or full-time, to get a productive part of the economy going, which in turn of course leads to people paying more tax.”
In the Commons, Ms Pochin argued removing the two-child benefit cap entirely rewards those who “play the system”.
She said birth rates are higher among foreign nationals, so Labour’s policy will mean a “significant amount of this additional expenditure” will go to households where at least one parent is born outside the UK.
The Runcorn and Helsby MP said: “Scrapping the two-child benefit limit does nothing to help hard-working parents who set their alarm clocks every morning and does everything to encourage families already on benefits to have more children in the full knowledge that the state will pay for them.
“Removing the two-child benefit cap without imposing any other restrictions, such as limiting it to working families with British-born parents, fails to incentivise work.
“It increases the support to non-working families beyond that given to working parents earning above the benefit level.
“So, those who work are being punished while those who play the system are rewarded.”
Mr Anderson, MP for Ashfield, added that “British people should be put first”.
The Bill will be further scrutinised by MPs and peers before it can become law, but the Government has said it wants to ditch the two-child limit from April.
The policy currently restricts child tax credit and universal credit (UC) to the first two children in most households, and campaigners have argued 109 children across the UK are pulled into poverty by the policy every day.
The change, if the Bill passes into law, would mean families can receive the child element of UC for all children, regardless of family size.
LBC has contacted Reform UK for comment.