Tom Watson is a peculiarity. Labour’s deputy leader is the only nonbeliever who was in Jeremy Corbyn’s first shadow cabinet and is still sitting there – much turmoil and many waves of resignations later.

This does not mean he is trusted by the Corbynites, many of whom have regarded him as a sworn enemy since the attempt to oust the Labour leader two summers ago. Yet Watson insists that their relationship is a good one. “Despite what people say. We text regularly. We talk about the kids. We usually have a lot of football talk. One thing we agree on is that we should spend less time in each other’s company at NEC [national executive committee] meetings, because the last one was nine and a half hours and it was torture.”

He claims to be “not remotely annoyed” that he will not be making a speech from the platform at the Labour conference and welcomes a proposal to create a second deputy leader, a position which would be reserved for a woman.

“I’m strongly in favour of it. We do need to strengthen our top team with strong women. Neither of us are going to go on for ever, and I think the leader after Jeremy should be a woman. So having a woman deputy leader with their own mandate from the membership, not there on patronage from the leader alone, would be very important.”

One of the hottest rows at that excruciatingly long NEC meeting was over rule changes which would make it easier for dissatisfied members to deselect Labour MPs as parliamentary candidates. Those pushing for mandatory reselection say that no Labour MP has a divine right to sit in parliament. Those opposed say it will lead to vicious and fracturing battles in local parties.

Tom Watson says he is ashamed about the antisemitism furore. Photograph: Wiktor Szymanowicz/Barcroft Images

“I am strongly against,” says Watson. “It will be very destabilising for the party and it will make it far harder to do an effective job in parliament. If all our MPs have to be back in their constituencies defending their positions in the way that mandatory reselection will ensure, they’re not going to be holding the Tories to account.”

He also fears that it would lead to an ideological purge of MPs who don’t fully subscribe to Corbynism and trigger a breakaway from Labour. “There’s a bigger issue for the party. We are genuinely on the cusp of power. We have a government that could collapse at any moment and the country needs us to be a functioning, united opposition. Labour has only ever succeeded as a broad church and the country needs us to be that broad church at this crucial point in our nation’s history.

“It’s up to me and” – he adds pointedly – “Jeremy to unify this party, to ensure everyone has a pew in this broad church.”

We suggest to him that the more zealous Corbynistas do not display much enthusiasm for the idea of a pluralistic party tolerating a wide range of views. “Well, I worry about it. There are too many groups of people in our party who feel unwelcome, unwanted or driven out. We’ve obviously had the sense that our Jewish members feel that they’re not welcome in the party.” He tells us he is “ashamed” that Labour’s summer was devoured by the furore over antisemitism and that the party still has much work to do to “rebuild trust with the Jewish community”.

He is also anxious about what is happening in some constituency parties: “I look at some of the newer MPs who are facing votes of no confidence and I think it’s so nihilistic to do that. I don’t want them to feel they’re under siege from small groups of people in their constituencies trying to shake the tree.”

Jeremy Corbyn must unify the party if he wants to become prime minister, Tom Watson says. Photograph: Hannah Mckay/Reuters

Some of the Labour MPs contemplating a split from the party will say that it is morally unsustainable for them to stand for Labour at the next election when they think Jeremy Corbyn is unfit to be prime minister. What does Watson say to them? “I’d say stay and fight your corner.”

They might retort “we fought, we lost, this is not the Labour party any more”. Watson shrugs. “You win some, you lose some. You’ve got to be resilient. Stand up for what you believe in. Fight.”

He insists: “It is the Labour party. It is a very different party, in a new context. I take you back to my original point. We are only successful when we’re a broad church. You look at our traditions from the Marxist tradition to ethical socialism to Christian socialism to classic social democracy. We’re only successful when those traditions are aligned and find an accommodation with each other.”

Does Corbyn actually believe that? “Well, look, he’s never going to be prime minister unless we do that.”

Brexit will be a big issue at the conference, one made even more salient in the wake of Theresa May’s humiliating debacle at the Salzburg summit. Is there any conceivable deal she could come back with which Labour would support? “Well, you’ve seen Keir’s six tests,” he says, referencing the tests set by Keir Starmer, the party’s spokesman on Brexit. Then he pleads: “Please don’t ask me every one in an interview.” What? He doesn’t know what Labour’s six tests for Brexit are? “I could probably give them a go. I don’t want to, just in case I get them wrong.”

The leadership’s current line on another referendum is noncommittal. “I still think the best way is for parliament to have a meaningful vote on the deal. And if parliament can’t agree, the implications of the deal should be discussed through a general election.”

This is the official line, but it may be crumbling. Today the Observer publishes a poll reporting overwhelming support for another referendum among Labour members. The big unions are moving in that direction too.

When pressed, Watson concedes this has a lot of force: “Jeremy and I were elected in 2015 to give the Labour party back to its members. So if the people’s party decide that they want the people to have a final say on the deal, then we have to respect the view of our members.”

Just in case we have missed the point, he repeats it: “If our membership speak and call for a people’s vote on the deal, then we have to respect it.” We get the impression that he is now talking not so much to us, as directly to Corbyn and his inner circle: “That’s what happens when you turn the party back to the members.” And he gives us a little smile.