Labour will fight for the benefit cap to be scrapped completely, Jeremy Corbyn has told the New Statesman.

The party's leader has over-ruled frontbenchers who suggested that Labour would back the cap in principle, but oppose its upcoming reduction from £26,000 to £23,000 in London, and £20,000 elsewhere.

Both Corbyn's predecessors, Harriet Harman and Ed Miliband, supported the cap.

When the new leader used his speech at the TUC conference a week ago to call for the cap's abolition, he was immediately contradicted by his own shadow work and pensions secretary Owen Smith and shadow equalities minister Kate Green, who insisted that it was still party policy to support it..

But Corbyn confirms for the first time that he will assert his authority on this subject. He tells the New Statesman’s George Eaton: “It’s what I’ve put forward as leader and I’ve made that very clear . . . We will now oppose completely the Welfare Reform Bill.

“In my own constituency, the benefit cap has had the effect of social cleansing, of people receiving benefit but the benefit is capped, therefore, they can’t meet the rent levels charged and are forced to move. It’s devastating for children, devastating for the family and very bad for the community as a whole.”

The move will rile many of his own frontbenchers who believe the total amount of benefits available to each household should be limited. However, although he opposes the household cap, Corbyn does not oppose the overall government welfare spending cap of £119.5bn.

In the interview, Corbyn also says that several crucial policy decisions will be put to a vote among party members at Labour conference, which begins this weekend. He has long advocated a system – similar to that used by the Lib Dems – of allowing the party membership more power to form policy.

For the first time in recent history, party conference delegates will be given the chance to vote on a motion on abolishing Trident, a stance endorsed by Corbyn but opposed by many in his shadow cabinet.

Asked whether unilateral nuclear disarmament would become party policy if the motion passes at conference, Corbyn replies: “Well, it would be, of course, because it would have been passed at conference.”

He also reveals that he would agree to introduce mandatory reselection (a system some fear would be used to oust “Blairite” MPs), if the party membership votes for such a mechanism. In spite of speaking out against mandatory reselection in the past, Corbyn says it would “absolutely” become “party rules” if activists vote in favour.

Corbyn also reveals that, while respecting the Good Friday Agreement, he supports the idea of a united Ireland. “It’s an aspiration that I have always gone along with ... I think that in Ireland the cross-border arrangements are working quite well, power-sharing is going through a hard time at the moment, it may or may not collapse, I don’t think it will, I think a deal of some sort will be struck before the end of this year and it will carry on through to the elections that are due.

“It has to be up to the people on both sides of the border in Ireland to decide what their future is. Nobody wants to go back to what happened in the 80s and early 90s.”

This stance could unsettle the party; both Jeremy Corbyn and his shadow chancellor, John McDonnell, have made headlines with controversial statements about the peace process and the IRA in the past.

On the controversial appointment of McDonnell, Corbyn says: "I always knew there was going to be some criticism made of it. He is a very close friend of mine, as everybody knows. He is a brilliant guy on economics and the ideas that go with it. I think it’s very important that the leader and shadow chancellor are thinking in the same direction and we’re certainly doing that. John has made a great start, setting out what his economic policies are."

>Now read George Eaton's interview with Jeremy Corbyn