Theresa May has refused to commit to giving MPs a vote on the final Brexit deal struck by the government during two years of talks with representatives of the other 27 countries in the EU.

Appearing before a committee of senior MPs, the prime minister also suggested her government was prepared to agree to some form of transitional deal, largely to help avoid a “cliff edge” scenario for businesses after a UK exit.

She said she would make a speech early in 2017 to set out her latest position on Brexit, but would not indicate when exactly the government would bring forward a written plan before triggering article 50.

May was pushed repeatedly on the question of whether MPs would be given a vote at the end of the process, once the final deal has been agreed, but refused to offer any commitment on the issue.

“Parliament is going to have every opportunity to vote through the great repeal bill on the various aspects of the relationship that we will be having with the European Union,” she replied after being asked by Hilary Benn, who chairs the Commons’ Brexit committee.

When the Labour MP repeated the question, May said: “It is my intention to make sure that parliament has ample opportunity to comment on and discuss the aspects of the arrangements that we are putting in place.”

That led Benn to ask the question again, this time saying he could not understand why it was so difficult for her to offer a clear answer.

“What I am saying is there will be an opportunity for parliament, of course, to consider when more details do become available how this is going to operate,” she said, before saying her priority was “delivering on the vote of the British people to leave the European Union”.

May appeared exasperated when the issue came up again later during her appearance at parliament’s liaison committee, in which she faced a series of tough questions on Brexit from the chairs of several high-profile Commons committees.

Andrew Tyrie, her Conservative colleague and chair of the Treasury committee, asked if she agreed with David Davis, the Brexit secretary, that British MPs should be at least as well informed as those in the European parliament. He pointed out that MEPs would have a vote on the deal.

She said: “We are very clear that we want parliament to be able to have the opportunity to debate and discuss. The European parliament has a specific role within the negotiations that is different to the role that the British parliament has.”

When Tyrie suggested that answer sounded like a no, May said: “There seems to be this idea that somehow we are not allowing parliament to do anything; we’ve made statements to parliament, there will be debates in parliament, there will be the great repeal bill ... we will make sure that parliament has the opportunity to discuss these matters but we will not be setting out on an hour-by-hour basis a running commentary.“It is my intention that parliament should have every opportunity to discuss, but I’m clear we deliver on the vote of the people.”

Pushed by Tyrie, who asked again if he should take that as a no, May said: “I gave the answer I gave, chairman.”

The clear decision by May to hint that there would be no final vote was attacked by Labour and Liberal Democrat politicians.

Keir Starmer, the shadow Brexit secretary, told the Guardian: “It is a pretty extraordinary step given that MEPs are guaranteed a vote and they can vote the deal down. David Davis has repeatedly said there will be no less scrutiny in the British parliament than in the European parliament.”

Starmer said that having no less scrutiny was a minimum demand from the Labour party and that required a vote, saying it was unacceptable that “MPs won’t vote but MEPs will”.

Referring to the government’s appeal of a high court ruling over having a vote on triggering article 50, he said: “So they don’t want a vote at the beginning and they don’t want a vote at the end.”

Tim Brake, the Lib Dems’ foreign affairs spokesman, said: “The European parliament will get a vote on the final Brexit deal. It would be absurd if the UK parliament and, more importantly, the British public were denied a say. Theresa May must stop trying to duck accountability by repeating empty platitudes.”

May also gave her clearest indication yet about the government’s plans with regard to a transitional Brexit deal, admitting that her government was prepared to consider an “implementation phase”.

She said: “When people talk about transition often different people mean different things by transition. There are some people who will talk about transition as a deliberate way of putting off leaving the EU; for others, transition is an expectation that you can’t get the deal in two years and therefore you’ve got to have a further period to do it.”

The prime minister said she would look to respond to British business but it would focus on helping them take on a new deal.

“When they talk about a cliff edge, they don’t want to wake up one morning with a deal agreed the night before and suddenly discovering they have to do everything in a different way,” she said. “So there is a practical aspect of how you ensure that people are able to adjust to the new relationship, which is not about trying to delay the point at which we leave and not about trying to extend the period of negotiation.”

However, May admitted that Britain could remain in the EU for an implementation period beyond the two-year article 50 cutoff, in order to give civil servants and businesses time to adapt.

The prime minister made the comments after Tyrie pointed out that article 50’s two-year deadline for departure related to the situation if no deal were reached. He suggested that successful negotiations could lead to a later date being agreed for when EU treaties cease to apply to the departing nation.

May also appeared to confirm that Whitehall was preparing for the “worst case scenario” of Britain leaving without agreement on its future relationship with the remaining 27-countries - possibly because a deal had been vetoed by the European Parliament. In that situation it might be the EU27 that needed to ask to extend negotiations, she suggested.

“We are looking at a variety of scenarios that could come forward in relation to the negotiation, the deal, the timing and what other opportunities would be there,” May told the committee. “We are looking at all the options.”

May was also questioned over immigration, during a tetchy encounter with Yvette Cooper, who chairs the home affairs select committee, over whether the government had a sensible migration target.

Cooper claimed the government was in a “bit of a mess on immigration”, but May insisted that the aim to reduce numbers to the tens of thousands and to keep international students in the figures were the right thing to do.

She also answered questions by the chair of the Scottish affairs committee, Pete Wishart, who asked about the push from his Scottish National party to keep Scotland inside the single market.

May said she would listen to proposals but was clear that it was a UK-wide negotiation and played down the idea of different deal for Scotland.

On the notion of a second independence referendum in Scotland, she added: “If Scotland were to become independent ... it would not longer be a member of the single market of the EU but also no longer a member of single market of [the] UK.”

The prime minister’s appearance was praised by Brexit-supporting MPs in her own party.

Dominic Raab said: “This was a calm and resolute performance. The prime minister made clear Britain comes to the negotiating table ambitious for a far-reaching post-Brexit deal that’s good for all sides, but capable of thriving whatever the response. Anyone who thought we’d be crawling back to Brussels with a begging bowl can think again.”