The Wigan MP Lisa Nandy has announced she will enter the Labour leadership race, with a stark warning to party members that “unless we change course, we will become irrelevant”.

Nandy, who has championed the needs of Britain’s towns, announced her decision to run in a letter to constituents, carried in the Wigan Post.

Setting out her pitch for the top job in an article for the Guardian, she took a dig at her rival Keir Starmer’s promise not to “oversteer” in the wake of last month’s general election defeat.

“Now is not the time to steady the ship or try not to oversteer,” she wrote. “What is needed are the hard yards of winning the argument inch by inch in town halls, workplaces and pubs. This is where we fight to regain people’s trust. The next Labour leader will have to be up for a scrap – willing to run to the places we are loathed, take the anger on the chin, make and win the argument.”

Nandy faces a considerable challenge convincing her fellow MPs that she has a chance of winning, after a YouGov poll this week suggested she was the first preference of just 6% of members.

The poll, commissioned by the Party Members Project, suggested Starmer was the clear frontrunner, with the leftwing candidate Rebecca Long Bailey in second place, and Jess Phillips, third.

Lisa Nandy at the Labour party annual conference 2015. Photograph: Gareth Fuller/PA

Long Bailey is likely to benefit from the considerable campaigning resources of Momentum, if, as expected, she emerges as the leading leftwing contender.

Momentum, a group set up to build on Jeremy Corbyn’s successful candidacy in 2015, has not yet decided who it will back, but a spokesperson said: “We have got this incredible people-powered campaign machine and we will be throwing it behind a leftwing leadership candidate.”

Phillips, the Birmingham Yardley MP, also declared her candidacy on Friday. Like Nandy, she stressed the importance of appealing to working-class voters who had deserted Labour.

“I wasn’t sure if I was going to stand in this contest, but listening to the debate in the days after the election, I thought, we’ve got to elect someone who gets it. Someone who understands how serious this defeat was. We’re a party named after the working class who has lost huge parts of its working-class base. Unless we address that, we are in big trouble,” Phillips said.

She tweeted a campaign video along with a statement saying that “politics needs honest voices” and urging people to join her campaign at her website.

I’m standing to be the next Labour Leader. Politics needs honest voices. Only when we are honest again, with ourselves & with the country, will we become the people who get to make the decisions. I can’t do this alone. Join me to help make things better at https://t.co/BCJG9DjidP pic.twitter.com/nhVxGSF5ml — Jess Phillips MP (@jessphillips) January 3, 2020

Phillips and Nandy will join Emily Thornberry and Clive Lewis as confirmed candidates. Others including Long Bailey and Starmer are expected to join the race formally in the coming days.

Phillips was first elected to parliament in 2015. She has achieved prominence with her campaigning on equality issues and tackling violence against women, and has at times been a fierce critic of the party’s direction.

In a statement announcing her candidacy, she said voters had lost trust in the Labour party and stressed the need for Boris Johnson to be challenged with “passion, heart and precision”.

She criticised the current leadership’s “woeful response” to antisemitism within the party’s ranks and Jeremy Corbyn’s ambiguity on Brexit.

Jess Phillips speaks in Parliament Square during the October 2019 People’s Vote demonstration. Photograph: Isabel Infantes/AFP via Getty Images

Phillips said: “We have got to be brave and bold and bring people with us, not try and look all ways. Trying to please everyone usually means we have pleased no one.

“Now is not the time to be meek. Boris Johnson needs to be challenged, with passion, heart and precision. We can beat him.”

She also made clear she would have no qualms in challenging the US president, telling a Channel 4 News: “Of course you have to be prepared to confront anybody if you are in any position of power … Being an ally means being honest. I would have absolutely no problem in confronting Donald Trump.”

Corbyn announced in the aftermath of last month’s election defeat that he would stay on as leader for a “period of reflection”.

Labour’s ruling national executive committee (NEC) will meet on Monday to set the timetable for the contest, which is expected to be completed by the end of March.

Phillips is calling for registered supporters to be allowed to participate in the contest at a low cost, such as the £3 paid by many who took part in the 2015 race that led to Corbyn’s election. In 2016, when Corbyn was challenged by Owen Smith, the NEC raised the cost to £25 and set a tight deadline for registering.

A spokesperson for Phillips’ campaign said: “The Labour party membership, affiliates and supporters will be looking to this contest as a moment we can turn the page on what happened in December. They will want a proper say on what comes next for Labour. They deserve nothing less.

“They’ll be looking to the NEC to ensure a process and timetable that respects the people who make this party what it is, the people who spent hours in the cold and rain during the election. They must get their say.”

• This article was amended on 4 January 2020. An earlier version incorrectly implied that Momentum was set up before Jeremy Corbyn’s election as Labour leader in September 2015. It was established the following month.