Jeremy Corbyn is now “completely secure” as Labour leader for years to come and can win a majority by reaching out to traditional working-class voters, says the party’s deputy leader, Tom Watson.

In an interview with the Observer, Watson calls on Corbyn’s allies to back away from unnecessary attempts to change party rules to shore up their leader’s position. Instead, he urges the party to focus on reaching “those people who doubted us or weren’t quite convinced” at the last election.

Watson, once seen as a prominent critic of the party’s left who a year ago warned Corbyn that his leadership had become untenable, said there was now “a highly enthused PLP [parliamentary Labour party] around him to take him through the years ahead”.

He said it meant there was no immediate need to change party rules. Some activists want to give party members more power on Labour’s ruling body and the right to nominate leadership candidates – both measures that would strengthen Corbyn and Labour’s left.

“Before the election, there was a sense of urgency around some of the activists ... to try to rush [rule changes] through,” Watson said. “Well, I think everyone knows now Jeremy’s position is completely secure as leader.”

It comes as Labour’s new chairman Ian Lavery, a Corbyn ally who replaced Watson in the post, warned that Labour was “too broad a church” and that MPs must “work very hard” to avoid deselection. He told the HuffPost UK that he wanted to look at “different ways and means” for selecting MPs.

However, Watson said the party now had to focus on winning back working-class voters in its traditional heartlands who have stopped backing the party.

“What comes out of it is a potential new alliance for Labour,” he said. “If we can bring [in] 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 I think we’ve got an election-winning alliance and I think it is an unbeatable one.”

His intervention will be seen as the first tentative attempt to encourage Corbyn and his team not to interpret the election result simply as a comprehensive endorsement of Labour’s leftwing prospectus.

It comes as one of the first major attempts to analyse Labour support warns that the “one more heave” approach cannot secure a strong majority. The study by the centre-left Policy Network thinktank, to be publishedon Monday, found that C2 social grade voters, typically earning between £21,000 and £34,000 a year, made up the key group that has so far proved resistant to Labour’s surge in support.

It found that 48% of voters in this income group voted Conservative last month, compared to 33% for Labour. Almost half of the group (47%) believe that Labour has moved further away from its “traditional working-class supporters”, with only 22% believing that Labour has moved closer to them.

Labour needs to win 64 seats to get a majority, more than twice its net gains from the last election. Almost two-thirds of those target seats have more C2 voters than more affluent ABs.

Watson said that the party would have to run a “slightly different campaign” at the next election. “We have got to give reassurance to those traditional, working-class communities,” he said.

The Policy Network report, co-authored by former Tony Blair and Gordon Brown adviser Patrick Diamond, suggests that C2 voters are currently most sceptical and have a less favourable view of the Labour party.

Tom Watson says party needs to shore up their leader’s position. Photograph: Andy Hall/The Observer

It found that Labour’s “core vote” is increasingly concentrated among the highest and very lowest earners in Britain. The polling shows that being a middle-income earner (£21,000 to £34,000) decreases the probability of voting Labour by nine points, compared to someone earning less than £14,000 a year.

It concludes that Labour needs to do more to dispel the perception of economic incompetence, convince its traditional base that it can negotiate a good Brexit deal and offer a more reassuring line on security.

The authors warn Corbyn against taking the “Bernie Sanders” approach by seeking to increase its support among groups that formed the core of the 2017 coalition: the professional middle class, economically precarious younger voters, and the poorest groups on very low incomes.

The co-authors, Diamond and Charlie Cadywould, said: “A ‘one more push’ approach at the next election may be enough to allow Labour to cobble together an unstable minority government, but much more is needed to win an outright majority even of one, let alone a comprehensive victory which would produce a two- or three-term government able to deliver radical reform.

“For Labour to win a majority, it can’t forget about the lower middle classes, and this polling shows it has a lot more work to do before it wins sufficient support from ‘making ends meet’ Britain.”

The research includes polling by Populus. It surveyed 2,511 people online between 2-5 June 2017, including extra 2015 and 2017 Labour voters, to ensure a robust sample size for its analysis. The overall results were weighted to reflect the 2017 general election result.