Senior MPs have called on the government to reconsider plans to make it easier for trans people to have their preferred gender legally recognised to ensure that the reforms are not detrimental to women’s rights.

Maria Caulfield, the Conservative party’s former vice-chair for women, said the parliamentary inquiry into transgender rights, which informed the consultation that is due to end on Friday, was “fundamentally flawed” and failed to consider the wider implications of the proposals for women.

The MP for Lewes, who sat on the inquiry, said she was writing to the minister for women and equalities, Penny Mordaunt, to ask her to extend the consultation on the Gender Recognition Act to ensure that women’s voices were heard. Mordaunt’s office declined to comment.

Speaking at a meeting of MPs with women’s rights groups at Portcullis House on Tuesday, Caulfield said the transgender inquiry was focused on the difficulties trans people faced in obtaining legal recognition of their preferred gender and “didn’t really look at the implications for women as a whole. I think that was fundamentally flawed”.

She said MPs should have more time to assess the concerns of women’s groups about the changes, such as how they might affect women-only spaces.

“I very much feel that the female side of the argument hasn’t really had a strong enough voice,” she said. “I don’t want to make legislation if we feel that there’s a group in society who feels that [it] is detrimental to them. I think it’s a fair comment that women’s groups do not feel that they’ve had their voice heard.”

A number of MPs including Conservatives Andrew Selous and David Davies, and Labour MPs Karin Smyth, Tonia Antoniazzi and Paul Williams attended the meeting with activists from Fair Play For Women, Woman’s Place UK and Transgender Trend, who said they and other women had faced online and real-world harassment for organising, speaking at and attending meetings to discuss the reforms.

Davies, the MP for Monmouth, said: “[The inquiry] failed to take evidence from women’s groups on what the impact might be of allowing people to change their gender without any checks and balances.

“Ideally I’d like to see [the consultation] stopped and the whole process restarted after the government and ministers have had a proper conversation with women’s groups about their rights to protection.”

Davies said he had been threatened with police action by another Conservative MP for holding meetings in parliament with women’s groups critical of the reforms.

LGBT+ Conservatives, the party’s official LGBT group, has called Davies’ comments that someone with male genitalia is “definitely not a woman” transphobic and abhorrent.

Selous said MPs were treading very carefully. “It is stifling freedom of debate if we can’t discuss these issues,” he said. “The fact that MPs can’t come and be briefed calmly and freely and without fear is appalling.”

Prof Stephen Whittle, the founder of trans rights group Press for Change, warned that many trans people would “become depressed and dejected” if reform was delayed. He said: “But in the end we will pull ourselves together and continue the campaigning. We know we have Labour behind this one, so will simply do our best to get them elected.”

Submissions to the consultation will be analysed by an independent company, which is due to report its findings to the government next spring, when ministers will consider what next steps to take.

The comments from MPs came as dozens of academics accused ministers and universities of ignoring and censoring experts concerned about the proposals.

In a letter to the Guardian, they write that some academics have come under pressure from trans activists and their own universities to not publicly raise their concerns.

The academics accuse trans advocacy groups of using suchwide ranging definitions of transphobia that “their effect is to curtail academic freedom and facilitate the censuring of academic work”.

• This article was amended on 18 October 2018 to amend a quotation after consultation with the person quoted and the writer.