Len McCluskey, the trade union leader, has launched a withering attack on Tom Watson, suggesting he would not be re-elected as Labour’s deputy leader if he faced a vote of the party’s members.

The Unite general secretary hit out at his former ally after Watson used a conference speech to urge the party to stop “trashing the record” of New Labour governments if it wanted to win elections.

In a speech that was seen as a rallying call to those sceptical of Jeremy Corbyn’s leadership, Watson told a cheering hall: “I don’t know why we’ve been focusing on what was wrong with the Blair and Brown governments for the last six years, but trashing our record is not the way to enhance our brand. We won’t win elections like that, and we need to win elections.”

McCluskey, who is a staunch supporter of the leadership, said he thought Watson had delivered an “extraordinary speech”.

“It confused me, it seemed to be saying that New Labour and the ‘third way’ was the way forward again. Now, it doesn’t surprise me because Jeremy Corbyn and John McDonnell are putting forward an alternative. The right wing of the party have got no vision so they are going back to yesteryear,” he told Sky News.

He said Watson’s speech had “no vision” and argued that Tony Blair’s governments did some good things but “we lost 1m manufacturing jobs, the gap between rich and poor continued, the seeds of inequality that we are seeing today were watered then”.

Tom Watson told Labour party delegates it was ‘time to be proud of our party’. Photograph: Christopher Thomond/The Guardian

Asked if Watson should seek to refresh his mandate after Corbyn’s overwhelming victory among members, McCluskey added: “Well, if Tom wants to try to refresh his mandate it would be interesting to see what happens.”

Watson said it was time “to be proud of our party”, because the Conservatives were beatable and the prime minister, Theresa May, could call an election any time. “We have to believe we can win and remember how much we achieve when we do,” he said.

At one point, Watson was heckled by an audience member. He responded by pointing at her and saying: “Jeremy, I don’t think she got the unity memo.”

Observing that Labour had “ended up sounding like we were anti-business”, he said: “Capitalism is not the enemy, money is not the problem, business isn’t bad. The real world is more complicated than that, as any practical trade unionist will tell you.

“Businesses are where people work. The private sector generates money to pay for our schools and hospitals. I don’t say this to win elections. I say it because it’s true, and people know that it’s true. That is why it wins elections.”

McCluskey denied the party was anti-business. He also addressed the row over the suggestion from Corbyn’s team that he does not believe immigration numbers should be reduced. The Unite boss said freedom of movement was an issue, but argued that the Labour leader had addressed it by talking about collective bargaining to protect workers’ pay rates.

“Because what is happening with migrant labour is it produces a cheap pool of labour that greedy bosses use to drive down wages,” said McCluskey. “I believe that the question of free movement of labour is a question not only in the UK but in Europe. No one talks of countries where migrant labour come from being denuded of skills. I believe issue of free movement of labour should be challenged.”