The 85-year-old singer said his cancer had "gone at the moment" and backed calls for a national screening test for men in the UK.
"I don't know whether it's going to come back," he said in an interview with Good Morning Britain.
"We can't tell those sort of things but we need to, absolutely, I'm convinced, get there, get tested, get checked."
He said he was diagnosed after a health check for his insurance ahead of a concert tour of Australia and New Zealand.
"The good fortune was that it was not very old, and the other thing is that it has not metastasised. Nothing had moved into bones or anything like that."
The singer, known for decades of hits including The Young Ones, We Don't Talk Anymore and Summer Holiday, described the lack of a national screening program in the UK as "absolutely ridiculous".
"We have governments to look after our country and those who live in that country, so I can't see how you can say, 'Oh we can do this, we can do that, but we don't do this for these people'," Sir Cliff said.
"We all deserve to have the same ability to have a test and then start treatments really early.
"It seems to me - I've only been for one year now in touch with cancer, but every time I've talked with anybody this has come up and so I think our government must listen to us."
The King last week said his cancer treatment would be reduced in the new year, and Sir Cliff said he was keen to join forces to raise awareness.
"I've been involved with many charities over the years and if the King is happy to front it for us, I'm sure loads of people, I certainly would join him."
11°C