Ms Mowlam says there is a rift between Blair and Brown
Ms Mowlam, who stepped down from Parliament at the last election, also confirmed a rift between Mr Blair and Chancellor Gordon Brown, saying the two men "aren't working together".
The programme, Cabinet Confidential, with Michael Cockerell, also shows Mr Blair's war cabinet which includes his director of communications and strategy, Alastair Campbell and newly-appointed head of government relations, Sally Morgan.
Speaking about the prime minister's relationship with the chancellor, Ms Mowlam told the programme: "When you have two people that aren't working together... it doesn't lead to positive, easy, decision making.
Crippling
"You know there's a battle going on and people support, or people go to, one side or the other.
"I think that is just crippling for government."
The two men have gone out of their way in the past to prove they are close - once appearing together on a radio programme.
Mr Blair told Mr Cockerell he had an open door policy when it came to his senior colleagues.
"I would be pretty shocked if the first time I knew a cabinet minister felt strongly about something was if they raised it at the cabinet table," he said.
"I would expect them to come and knock on my door and say, 'Look, Tony, I've got a problem here. I disagree with that.'
"And that happens from time to time and then you sit down and work it out."
Ms Mowlam also comes under attack from Deputy Prime Minister John Prescott during the programme.
During the programme Ms Mowlam also suggests unelected advisers have more power than the cabinet in relation to the prime minister.
"They seemed to be operating instead of the cabinet," she said.
Advisers
"He makes decisions with a small coterie of people, advisers, just like the president of the United States.
"He doesn't go back to cabinet, he isn't inclusive in terms of other cabinet ministers and if he really wants to get the support of the public and the support of Parliament there has to be more people included."
Labour MP Graham Allen, who has written a book entitled The Last Prime Minister - Being Honest About the UK Presidency, said:
"The only surprising thing about Mo Mowlam's comments is that it has taken her so long to realise one of the central realities of British politics," he said.
"The sooner Cabinet ministers and former Cabinet ministers face the truth, the sooner we will be able to work out a way forward by strengthening other British political institutions to contain the British Presidency."