The Labour party is in “big trouble” and could see its support fall further after its heavy defeat at the general election, Alastair Campbell has said.

Tony Blair’s former director of communications said he believes the Labour party needs to embark on a debate about its future that should have taken place before the leadership contest.

Speaking on the Andrew Marr Show on BBC1, Campbell said: “We are in big trouble, and we are in big trouble in the UK, which is why this leadership election is very very important. I wish we were having the election at the end of the debate, not instead of the debate. But we have to understand this may not be the bottom.”

Campbell spoke about Labour’s future as he related a story about his last contact with his friend Charles Kennedy, the former Lib Dem leader who died last week from a haemorrhage related to his alcohol problems.

Campbell said Kennedy had texted him to say they should discuss forming a new progressive, centre-left unionist party in Scotland after the SNP won 56 of Scotland’s 59 seats.

He said of Kennedy, who lost his Highlands seat in the general election to the SNP: “He basically [thought] that that the Labour party and Lib Dems up there are knackered.” Campbell then said Labour was in trouble across Great Britain.

Liz Kendall, one of the Labour leadership contenders, has hit back at her rival Yvette Cooper, who accused her last week of having swallowed the Tory manifesto. Asked on the Andrew Marr Show which parts of the Tory manifesto she would spit out, Kendall said: “The only thing I have swallowed is the sheer scale of the defeat that we faced at the election and the huge changes we need to win again.

“People didn’t trust us with their money or on the economy and we didn’t set out a positive enough vision for the future of the country that everyone could feel part of. It is the person that can answer those questions that’s going to win the leadership election to win the country in 2020.”