Laura Pidcock, the Labour MP for North West Durham, has told an interviewer she would never hang out with Tory women because she considers them the enemy. Pidcock is both young – she’s 29 – and female: she didn’t get where she has by smiling sweetly. She is a fighter. Even in politics, these are not attributes widely admired in young women. Good on her.

She was elected only in June, so she had barely a month in the Commons before everyone went off on holiday. All the same, she still had time to make a maiden speech. It was just after the abysmal moment when some Tories chortled at the prospect of continuing the freeze on public sector pay. The anger with which she rounded on Tories and accused them of enjoying other people’s poverty went viral. So it’s not exactly a surprise to learn that she sees all Tories as the enemy.

And no wonder she’s angry. Her part of Durham sits north of the city, amid the wreckage of industrial England. In her maiden speech, Pidcock said 16,500 people in County Durham, many of them in work but on low pay and zero-hours contracts, had relied on food parcels at some point in the past year. She almost certainly has an ally – not that she would necessarily appreciate it – in the archbishop of Canterbury. When Justin Welby was Durham’s bishop, he was at least as angry as she is.

So there’s no doubt that she is justified in being enraged by the smug complacency she sees on the other side of the Commons chamber. It’s just that they are not all the enemy.

Pidcock thinks the Commons is fusty and musty, and deliberately intimidating. She thinks, as she said in June, that “the clothes, the language, and the obsession with hierarchies, control and domination are symbolic of the system at large”.

Most new MPs, whatever their politics, would agree. Soon some of them, not only Tories, will settle into the comfortable embrace of the plenitude of bars, the entertaining gossip, the sense of privilege and entitlement that slowly encrusts long-serving members of parliament and turns the place into a toothless club rather than the cockpit of the nation of, say, Michael Gove’s imagination.

Others learn to exploit the curlicues of procedure to discomfit the government with unexpected votes or amendments to bills (Pidcock should look at the record of the 1980s Militant MP Dave Nellist, who was a master of procedure, and sometimes very funny, as well as often angry). Although reforms have sadly ironed out many of the opportunities for smart backbenchers to ambush the other side, other opportunities, more transparent, such as the greatly strengthened select committee system, have opened up.

The most unexpected friendships often grow between members out of step with their own party

The joint effect of the new power of select committees – which have to unite their cross-party membership behind a single report – and the slender majorities and uncertain loyalties of the past fractured political decade has been the growth of ad hoc cross-party alliances. Pidcock must know this can work, because in the few short weeks that she has been an MP, her colleague Stella Creasy played a blinder, combining well-established working relationships with like-minded women across the Commons (there are Tory feminists, Laura) and exploiting her understanding of procedure and the vulnerability of a government without a majority to force it to accept that women from Northern Ireland are entitled to free abortions on the NHS.

Creasy’s success points to a basic lesson: any MP who wants to maximise their effectiveness at Westminster must exploit to the limit the potential of alliance. Every MP, wherever they sit on the political spectrum, is a potential friend if there’s something you both want to get done. Denouncing everyone who’s not in your team feels good. It pleases your voters. But it doesn’t get things done.

Here’s another thing. Holding passionate political beliefs is, frankly, a minority interest. I know, hard to believe. Pidcock might be surprised to find that, exiled from her distant constituents in County Durham, she comes to admire, maybe even to have some fellow feeling for, others who feel differently but as passionately. Anyone who’s had the good fortune to see James Graham’s play This House, about the Labour and Tory whips’ offices in the 1970s Labour government, will know the truth of this.

The most unexpected friendships often grow between members out of step with their own party. Right now, Pidcock would surely throw herself from St Stephen’s Tower before asking a Tory to be godfather to one of her children. Yet (she says because of a pre-Westminster friendship) the former Tory high flier Jonathan Aitken is godfather to Diane Abbott’s son. The SNP MP Mhairi Black and Pidcock’s colleague on the Labour benches Jess Phillips both acknowledge a certain liking for Jacob Rees-Mogg. Jeremy Corbyn is appreciated by some of the wackiest Tories for his courtesy and the depth of his knowledge of unexpected subjects (especially the labour politics of South America). It is another inalienable truth of Westminster politics that your real enemies are not across the chamber, they’re sitting behind you.

But Pidcock is on to something. One of the hardest parts of Westminster politics is staying true to what you believe while being highly creative about how you achieve it. The next few years of unstable majorities offer the astute operator the chance of scoring some genuinely life-changing political hits. What her constituents need her to be doing is not talking about hating the other side. They need her to be assiduously attentive to the unglamorous business of scrutinising the Brexit legislation. There are no headlines in protecting workers’ rights or environmental regulations. It will take application and alliances. It may even require friendships.

Anger is indispensable. But hatred doesn’t get you anything except a grovelling interview on Skwawkbox.

• Anne Perkins is a Guardian columnist