In his first interview since his spectacular fall from office with Peter Mandelson, Mr Robinson also claims the Prime Minister is just as interested in "spinning" policies as the policies themselves.
The millionaire MP's comments will be made in Blair's Way, a Channel 4 documentary to be screened tomorrow night, which assesses the impact of Mr Blair's leadership style.
It will be preceded tonight by another Channel 4 programme in which a former adviser of the late Labour leader John Smith claims Mr Blair's predecessor would have encouraged a more "consultative approach" to government. In If John Smith Had Lived a Labour MP admits that he does not believe he would have won his parliamentary seat if Mr Blair had not become leader. It also includes claims that Mr Blair would "bang his head against his desk in frustration" at the slow pace of internal party reform under Mr Smith's leadership.
Mr Robinson - whose pounds 373,000 home loan led to Mr Mandelson's resignation from the Cabinet, and one of the blackest periods of the Government to date - will say that Mr Blair's style is similar to that of Margaret Thatcher. "It seems to me Tony's taken the Thatcher model a bit further really and the role of Cabinet is very restricted indeed ... some of the cabinet meetings only last 20 minutes for example. In the old days they would go on for hours," he says.
"He's also very interested in policy and he's also very interested in the presentation of policy and the two are pushed parallel in his evaluation of it."
Ron Davies, who was forced to resign as secretary of state for Wales over the Clapham Common affair, also tells the programme that Mr Blair's grip on the Government is total.
"When you arrive at Cabinet, basically the decisions are taken and it's the final collective seal of approval," he says.
Tonight's John Smith programme, which marks the fifth anniversary of his death from a heart attack, addresses for the first time one of the most sensitive issues within the Labour Party. Some Blairite MPs say privately that a Smith leadership would not have transformed the Labour Party in a fundamental way and might not have achieved outright victory at the last election. Stephen Twigg, whose defeat of the former Tory cabinet minister Michael Portillo was the most spectacular result of the 1997 election, will say that he would not have won his seat if Mr Smith had remained leader.
"I don't believe it's likely that I would have been an MP in Enfield Southgate without Tony Blair and New Labour," he says.
"I think we would have done very well, I think we would have succeeded in winning all sorts of votes that we didn't win before. But I think that New Labour itself and Tony Blair's leadership were crucial in constituencies like mine."