The government is to waive the planned fee for EU nationals living in the UK to apply for settled status after Brexit, Theresa May has said in an update to the Commons in which she again rejected a second referendum and an article 50 extension.

Making a statement to MPs after her Brexit deal was voted down by a vast majority last week, the prime minister laid out what she described as the lessons from a week of talks with other parties.

However, beyond the change to the fee policy, the other lessons primarily saw May entrench her existing positions, prompting Jeremy Corbyn to liken the Brexit process to “Groundhog Day”.

Under the planned scheme for EU nationals to apply to stay in the UK, which is currently being piloted, those aged over 16 have to pay £65, with a cost of £32.50 for anyone younger.

May told MPs she had listened to “powerful representations” on the scheme. “I can confirm today that when we roll out the scheme in full on 30 March, the government will waive the application fee so that there is no financial barrier for any EU nationals who wish to stay. Anyone who has applied during the pilot phase will have their fee reimbursed.”

May said she had met MPs and other parties “in a constructive spirit, without preconditions”, and criticised Corbyn for refusing to take part unless she ruled out a no-deal departure.

Among six elements of her revised Brexit strategy laid out by the prime minister, including the fee waiver, was to argue that the only way to stop a no-deal departure would be to either vote through a deal or revoke article 50.

She also dismissed the idea of seeking an extension to article 50, saying this was just “deferring the point of decision” and would probably be rejected by the EU.

May also dismissed the idea of a second referendum as something that would “damage social cohesion by undermining faith in our democracy”. She also argued it could not command a majority in parliament.

The other three issues laid out by the prime minister were efforts to reassure MPs on the Irish border backstop; giving more details on a future relationship, including confidential committee sessions to allow MPs to be kept informed; and guarantees on environmental standards and workers’ rights.

“The process of engagement is ongoing,” she said. “In the next few days, my ministerial colleagues and I will continue to meet with members on all sides of the house, and with representatives of the trades unions, business groups, civil society and others as we try to find the broadest possible consensus on a way forward.”

In response, Corbyn said May appeared “not to have come to terms with the scale of the defeat in this house last week”.

The Labour leader said: “The prime minister seems to be going through the motions of accepting that result, but in reality is in deep denial.

“The logic of that decisive defeat is that the prime minister must change her red lines because her current deal is undeliverable. So can she be clear and explicit to the house: which of her red lines is she prepared to move on?”

A series of other MPs welcomed the decision on the fees but condemned May for what they said was her intransigence.

The Labour backbencher Yvette Cooper, who has tabled an amendment seeking an extension to article 50, said the prime minister was showing no signs of genuine flexibility.

Cooper said: “If she’s serious, why not give parliament a say before we’ve finished article 50 negotiations, not after, and why not put to parliament some votes on her red lines, including a customs union? Otherwise how can any of us believe a word she says?”