Tom Watson’s Glastonbury experience this year could scarcely have been more different from the misery of his festival outing 12 months ago. Back then, he managed only 14 soggy hours before receiving a mass of calls telling him that an attempt to topple Jeremy Corbyn was under way.

This time round, he was at the festival from start to finish and was able to experience the excitement generated by Labour’s surprisingly strong election performance. At this year’s silent disco, he says he sang his own rendition of the Corbynista chorus “Oh, Jeremy Corbyn”, to the backing of the White Stripes.

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“All the kids were coming up to talk about the Labour party,” he said. “Last year we were in mud, and people couldn’t believe we had just lost the EU referendum. This year I have never known the excitement about change. It was universally friendly, all of it, and a real sense of hope and energy. It was quite inspiring.”

Throughout his interview, Labour’s deputy leader repeatedly praised the “terrifically exciting” result that Corbyn achieved. There is also a clear sense from him, however, that the party must not get carried away and should now turn to winning back the voters it lost in June.

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“You shouldn’t draw easy conclusions from results like this,” he says. “There is a lot of analysis that is still to be done. But there are some rather obvious things. People under 40 were worried about the future of public services and genuinely wanted a fairer society and they have a government that doesn’t really believe in that.

“The electorate wrenched the agenda from every politician and spoke with passion about a whole array of issues. It was all about the government’s record – school failure, hospitals, kids’ jobs, inability to lay down roots, quality of life – I’ve never had so many issues raised. And so I think we need to understand that.”

Watson suggests that it is traditional working-class voters – the sort of people he represents in West Bromwich East – that have been leaving the party and that Labour now needs to convince. While Corbyn has won over the very poor, the young and well-off voters in metropolitan areas, this group remains unconvinced by Corbynmania.

“What comes out of it is a potential new alliance for Labour,” he says. “If we can bring these young voters, enthuse them to stay with us and then give greater reassurance to our traditional working-class voters, some of whom left us on issues like policing and security, then we’ve got an election-winning alliance, and I think it is an unbeatable one. We’ve got a lot of work to do, but I can see a way through.

“Our traditional base still stuck with us in large numbers, but we need to do a bit more work to reach those people who doubted us, or weren’t quite convinced. “I think what we’re going to find is that the Conservative manifesto was laced with hubris and they were too arrogant to listen. I guess the lesson is the lesson from the Tories, which is you can never take voters for granted. We’ve got to really listen to them and I am certain we will. I think Jeremy understands that we need to address the concerns of some of our traditional voters.”

Facebook Twitter Pinterest Tom Watson at Glastonbury 2017. Photograph: Nigel Roddis/EPA

Watson’s gentle suggestion that the party must not draw the wrong conclusions from the election is a point made more stridently in private by other Labour figures, concerned that Corbyn’s team will see it as a licence to endorse an even more unapologetically socialist programme next time.

Watson says: “You should never fight the last election, that’s for sure. There is no doubt that we will have to run a slightly different campaign, but we know where we have got to be – we have got to give reassurance to those traditional, working-class communities. [A majority] is very possible now.”

He also says Labour will have to be ready for a “Rolls-Royce operation from the Tories”, rather than a repeat of the disastrous election campaign that saw hopes of a landslide end in the loss of a majority.

“It also means we have to be very focused in what are now our key offensive marginal seats. That is why we will have a busy summer, because Jeremy is going to visit a lot of them.”

He concedes that Labour has to “develop our post-Brexit policy”, which remains vague. “We accept the current arrangements are going to change. There won’t be free movement of labour like you have now, there will be new restrictions and it will probably be based around some work permit allocation.”

He also raises the concept of different regional quotas for overseas labour, allowing places that need workers to take more than areas that have no shortages. “Arguably the two areas of the country where you could claim there’s a shortage are London and Scotland. If you can accommodate those demands while managing in other regions, maybe that’s possible.”

Watson supports Corbyn’s big post-election decisions. He believes that handing Owen Smith, a former leadership challenger, a post in the shadow cabinet was a clear enough gesture from Corbyn that he was reaching out to moderates.

He also chastises Chuka Umunna, the former shadow business secretary, for engineering a vote in support of staying the single market and splitting Labour – and backs Corbyn’s decision to sack frontbenchers who joined the rebellion. “Leaders have to lead, chief whips have to instil discipline, and everyone knows how it works,” he says.

He is more wary, however, of new Labour rule changes being circulated before its autumn conference that would give the left more power – by increasing local party representation on its ruling body and allowing them to nominate leadership candidates. He urges restraint from Corbyn’s buoyant supporters.

“I don’t know where we’re headed on that,” he says. “What I do know is, there’s no rush. It seemed to me that before the election there was a sense of urgency around some of the activists ... to try to rush it through. Well, I think everyone knows now, Jeremy’s position is completely secure as leader. He has had a unified PLP [parliamentary Labour party] around him since his second election win, more or less, and now he has got a highly enthused PLP around him, to take him through the years ahead.

“I am personally in favour of party reform and giving members a greater say, but I don’t think a particular faction should impose the rules. I think you should consult the party and take your time over it.”

In the medium term, he says, there is a case for ending the payment of a one-off fee to allow people a vote in a Labour leadership contest – a group known as “registered supporters”.

“There are elements of the current system that are unstable – none of this is new. But I think most people think the registered supporters’ scheme is a bit of an anomaly, and that could probably go by a unanimous decision.”

He acknowledges that a lot has changed since the last Labour conference, when he was praised by many MPs for a speech lauding the achievements of Blair and Brown and calling on the party to focus on power over protest – seen as a dig at Corbyn’s leadership.

“The difference between now and then is there is a potential route to government with a new alliance of younger voters and bringing back some of our traditional voters we lost,” he says. “That’s absolutely inspiring – and it’s worth all of us throwing the kitchen sink at.”