The former Treasurer of the Britain Stronger in Europe campaign has lashed out at David Cameron's former aide Sir Craig Oliver, branding him the "dead hand of Downing Street". He claimed putting him in charge of the campaign had been a "mistake".

Speaking on Peston on Sunday, Roland Rudd, brother of Home Secretary Amber Rudd, said Sir Craig had failed "miserably" in putting forward the "positive case" for remaining in the European Union ahead of the historic British ballot on June 23.

He also accused him of focusing on "Conservative party management" rather than "winning the campaign".

"I think Craig is a very bright guy, able guy, but he, in a sense on behalf of the prime minister, ended up running our campaign and, however talented he is, that was a mistake," he told the programme.

"There was no blue on blue, which was an extraordinary mistake, it was about Conservative party management rather than winning a campaign.

"So if you allow the 'dead hand' of Downing Street to really dictate the campaign then of course that type of decision is going to be made in the interest of a party rather than in the interest of what is really needed in terms of the referendum."

He also condemned key failings of the Remain campaign to address immigration concerns, which became a factor of critical importance in the Vote Leave victory.

"We were not independent enough in terms of putting forward a positive campaign and to talk about immigration," he said.

"There was a sort of shut down from 10 downing street on talking about immigration and that was a huge mistake."

roland rudd peston on sunday
Roland Rudd speaks on ITV's Peston on Sunday on 2 October ITV

However, Sir Craig Oliver said managing internal party conflicts in the run-up to the historic vote had been extremely challenging, pointing the finger at then Home Secretary Theresa May.

"It was very difficult in the lead up to the campaign having a Home Secretary who did not reveal what side she was on," he told The Andrew Marr Show on Sunday (2 October).

"When she did reveal which side she was on, it was 51/49 and very equivocal."

Craig Oliver Andrew Marr
Sir Craig Oliver on The Andrew Marr show on Sunday 2 October BBC

He also blasted Michael Gove following accusations in his new book—Unleashing Demons: the Inside Story of Brexit—saying he had "faulting ambition and a preparedness to mislead".

Defending the allegations, Sir Craig said: "Let's look at some of the things that happened and why I described him in that way.

"Two days before he announced he would be the chair of the Leave campaign, he told the prime minister he wouldn't play a leading role in that.

"When he was leading that campaign, that was almost setting itself up as an alternative government that was questioning policies that were only tangentially related to Europe.

"He questioned the integrity of the prime minister saying he was corroding public trust, now that was concerning to us and not behaviour that we necessarily expected from him."

Sir Craig Oliver Andrew Marr
Sir Craig Oliver on The Andrew Marr show on Sunday 2 October BBC