MPs have slammed the “unacceptable” prospect of parliament not being given a vote on the final Brexit deal until after the UK has left the EU.

Brexit Secretary David Davis predicted on Wednesday morning that a deal would unlikely to be signed until the very “last moment” before the UK leaves the EU in March 2019.

Asked by the Commons Brexit Committee if that meant parliament may not be given the chance to approve or reject any deal struck with Brussels until after Brexit, Davis said: “Yes. It could be.”

Theresa May told the Commons during prime minister’s questions she was “confident” that there would be time for a meaningful vote before Brexit.

A spokesperson for the PM added later: “A final deal will be agreed before before we leave and MPs will get a vote on it.”

Downing Street said the EU’s chief negotiator had said he expected a deal to be agreed by October 2018.

Asked why Davis had therefore predicted a deal would not be signed until the very minute before the UK was due to leave the EU in March, the spokesperson said: “The secretary of state was asked a lot of hypothetical questions.”

Brexit minister David Jones assured MPs in February that the vote would take place before the UK leaves the EU, not after.

“It will be a meaningful vote. As I have said, it will be the choice between leaving the European Union with a negotiated deal or not,” he said.

Labour MP Chuka Umunna said Davis’ comments were “in clear breach” of what Jones had told parliament.

Shadow Brexit Secretary Kier Starmer said the government had to “urgently clarify” its position as parliament must “not be side-lined”.

“David Davis and Theresa May’s comments only add to the confusion and chaos over the Government’s approach to the Brexit negotiations,” he said.

“Labour has been clear from the outset that Parliament must have the final say on the terms of Britain’s exit from the European Union before March 2019.”

Former Conservative cabinet minister Nicky Morgan told the BBC it would be “completely wrong” for a vote to be delayed until after Brexit had already happened.

“It’s completely pointless to have such vote at that stage and so its clearly unacceptable,” she said.

Lib Dem Brexit spokesperson Tom Brake said Davis’ comments were a “shameful attempt to force through an extreme Brexit and ride roughshod over our parliamentary democracy”.

“David Davis’ reputation as a champion of parliamentary sovereignty now lies in tatters,” he said.

Labour MP Seema Malhotra, the member of Brexit committee who asked Davis when the vote would be, said that would the government was treating parliament with “contempt”.

“Time and time again they are desperate to avoid scrutiny. We were promised a ‘meaningful’ vote on the deal, it beggars belief that it may well come after we leave the European Union,” she said.

Speaking to the committee, Davis said he expected the talks to go right down to the wire.

“It’s no secret that the way the EU makes its decisions tends to be at the 59th minute of the 11th hour of the 11th day and so on. That’s precisely what I expect to happen here” he said.

“If there is a time limit on a negotiation. The [European] Union stops the clock. It assumes it’s still at 11.59 until it’s concluded, sometimes over the course of 24, 36, 72 hours thereafter. It will be a lot of pressure. It will be very high stress. Very exciting for everyone watching.”

It will be a lot of pressure. It will be very high stress. Very exciting for everyone watching.”David Davis on the final moments of the Brexit talks

Earlier this year, May agreed to give UK MPs a vote on the eventual deal before it is then voted on by members of the European Parliament.

Davis told MPs today the likelihood of a the UK leaving the EU with a “hostile” no deal was “off probability scale”.

However he said the option of walking away with no deal had to be maintained otherwise the EU would have the UK “over a barrel”.

“No deal is an option, we have made that clear. It is not our preferred option, we want a deal,” he said.

We leave no-deal as an option literally right up to the moment of signing because it would not be the first time in European negotiations where sudden, last minute claims come in because they think they’ve got you over a barrel.”