The operation - broadcast live by BBC News - came during a two-year investigation into allegations the Christian singer sexually abused children.
The case was dropped last week by the Crown Prosecution Service which said there was "insufficient evidence" to prosecute the 75-year-old.
The BBC has apologised for distress caused to Sir Cliff by its coverage.
South Yorkshire Police has apologised over its handling of the investigation.
Sir Cliff said he was considered taking legal action for the "gross intrusion" into his privacy.
Speaking on ITV's Good Morning Britain, he said those subject to an investigation for sexual crimes should not be named unless they are charged.
The musician added: "There must have been illegal collusion. I've never known, I don't think, investigations take place with lighting and cameras and special angles for the helicopter - it just seems ridiculous.
"I feel I have every right to sue because, if nothing else, definitely for gross intrusion of my privacy."
Meanwhile, speaking during an interview with ITV's Loose Women programme which was broadcast on Wednesday, he also acknowledged the support of friends who had stood by him, including Sir Elton John, Tony Blair and the late Cilla Black.
Talking to television presenter Gloria Hunniford, he said: "All my friends, people I have met in Barbados ...the thing that has really been uplifting for me is that nobody can or will believe it but I still had to survive it myself.
"Only people who go through this can possibly know what it has felt like. I cannot even describe it, it wouldn't be possible. I have done my best to describe what it was like but it is never going to actually [express] the total loss of everything..."
Sir Cliff also recalled a diary entry he made prior to the case against him being dropped to highlight the emotional toll the investigation had on him.
He said: "I seem to be disappearing. Every time, I would wake up in the morning and I would go and wash my face I would look in the mirror and think 'there is this old geezer looking back at me'.
"I seemed to be more lined [wrinkled]. It may just be a psychological thing and part of the stress factor that you suddenly think 'I am going to the dogs'."