The Northern Ireland Affairs Committee is investigating the circumstances surrounding the on-the-runs controversy.
Last week retired Detective Chief Superintendent Norman Baxter, during his evidence, claimed Downing Street called for two men suspected of attempted murder to be released by police after it was contacted by Sinn Féin president Gerry Adams in 2007.
Speaking on Wednesday, Sir Hugh said he would be "staggered" if one of his senior officers called for the release of a suspect after a call from the Prime Minister's office.
He told the committee of MPs: "At no time did Number 10 ever try to influence my decision making.
"At no time did any secretary of state - and I had four of those - try to influence me.
"And at no time did any official from the Northern Ireland Office (NIO) ever try to influence my operational decision making.
"And had they, I would have made it public immediately."
He continued: "I am very concerned at the suggestion that at any stage at any time one of my senior investigators was put under any pressure to release serious terrorist suspects.
"It did not happen in my judgement and I would be very, very surprised if any such call was made in that regard.
"That having being said I would have been surprised if Mr Adams did ring Mr Blair to complain.
It was not unusual for politicians of all sides to complain about what the police service was doing - both loyalist and republican.
Sir Hugh Orde
"It was of course their right to do that and I would have expected to have been advised of that.
"So Number 10 or probably the NIO may have called to advise that, on that occasion, Mr Adams had been complaining.
"That is important because complaints from senior politicians of whatever side can have operational implication. There may be public order implications for example that we would need to consider.
"But never did anyone try to influence the due process I was charged with delivering.
"I would not have expected, and I would be staggered if this happened, that an assistant chief constable would tell a detective chief superintendent to de-arrest people."
Later in the hearing, Labour's former Northern Ireland secretary from 2007 to 2010, Shaun Woodward, said he was surprised at the outcome of the Downey judgment and added the administrative scheme was lawful.
"I remain astonished that these letters can be used to take the force that they did, can be used to take the interpretation that they have."
The chairman of the committee, Lawrence Robertson, said once the mistake in sending the letter to Downey had been discovered it was hard to remedy because telling Downey would mean alerting him to the fact that he was wanted in the UK.
Mr Woodward added: "It was a mistake, the problem is the mistake, for the victims involved in this, is appalling and indescribable."
He said in 2007 he was meeting a regular procession of politicians, particularly from the smaller parties, warning of trouble with Stormont's power-sharing administration.
He added critics needed to consider the administrative scheme in that context.
"There were real problems there that were going to need to be dealt with."
He added: "The big issue was a political process that was falling apart at the seams."
DUP MP Ian Paisley, in contrast, said they represented the halcyon days of a new administration.
Mr Woodward said there were repetitive conversations during his period as Northern Ireland secretary about how to resolve the anomaly over on-the-runs.
"They were always parrot repetitive in nature because there was not a law."
We want to get to the truth of the matter of what exactly happened.
NI Affairs Committee chair
Ahead of Wednesday's hearing, the chairman of the committee stressed the importance of the proceedings being held in public after requests were made for evidence to be given in private.
Speaking to Frank Mitchell's U105 mid-morning show MP Laurence Robertson said similar requests were made in every enquiry held by the Northern Ireland Affairs Committee.
Mr Robertson did not say who had made the requests.
He said: "One of the very important things we felt was that evidence should be heard in public.
"Sometimes we do get requests - not just on this inquiry but all inquiries - to have a chat with us in private.
"Occasionally we do this if we think it is worthwhile, but we do try to hold everything in public."
He added: "One of the problems about the on-the-runs issue was the accusation that it wasn't known by very many people at all, certainly I don't think the public knew about it and I certainly didn't.
"And that is the thing we want to overcome."
MPs launched their inquiry after it emerged that on-the-runs had been sent letters from the NIO informing them that they were not wanted.
It came out following the collapse of the John Downey case - who was charged in connection with the Hyde Park bombing in 1982, something which he denied.
He was mistakenly informed by the PSNI in 2007 that there was no interest in him from them, or any other police force across the UK.
As well as the Westminster committee's investigation, the Policing Board and the Police Ombudsman are conducting enquiries.
Prime Minster David Cameron has also ordered a judge-led investigation in the scheme.