Mr Brown, 54, was a pupil at a grammar school in Manchester in the 1970s where Talbot taught biology before going on to establish a career as a TV weatherman.
The singer said he went on a school camping trip organised by the teacher in 1977 or 1978 when he was 14 years old.
Edinburgh-born Talbot, 67, is on trial at Lanark Sheriff Court, accused of indecently assaulting several teenage boys on school trips to Scotland.
He is also accused of lewd, indecent and libidinous practices and behaviour towards a boy aged 12 on a trip.
Talbot denies the charges against him.
Mr Brown, who told the court he was self-employed as a singer and songwriter, said he had got on with Talbot before the camping trip.
He said: “He was possibly one of the only teachers who didn’t stick (cane) me.”
The witness said Talbot would regularly talk about trips during class but would only invite certain people.
“Mr Talbot did these trips and he decided who went,” Mr Brown told the court.
“You couldn’t just put your name down and say you were going.”
The witness said he did not know exactly where they had camped on his trip, but between 12 and 20 pupils had left school on a Friday afternoon in a minibus with Talbot.
When they arrived the area was covered in snow and they cooked dinner.
Mr Brown said: “While we were eating he said he was going to take someone to the pub.
“I think everyone probably wanted to go.”
The singer said one of the friends he was sharing a tent with had a “bit of bum fluff, a kind of moustache” and he was picked to go with Talbot because he looked older.
Mr Brown said the pair drove to a pub while the rest stayed behind.
He added: “We had bottles of rum anyway, we were told by Mr Talbot it was cold and we’d need it.
“We were told to make sure we had some with us.”
Mr Brown said when they returned his friend came back to the tent and tried to get into his sleeping bag.
He told the court: “Five minutes later Mr Talbot popped his head in and said: ‘I thought you were going to stay in my tent tonight?’”
The boy went with Talbot and Mr Brown “didn’t really think anything of it at that point”.
Asked what happened next by prosecutor Imran Bashir, Mr Brown said the boy had come back into the tent “in a state”, and had claimed that the defendant had tried to perform a sex act on him.
Mr Brown said: “I’ve never forgotten it, I was shocked.”
The next day the group went for a walk in the snow and Talbot suggested putting snow in a boy’s pants, Mr Brown said.
“We must have been naive. I think kids now would’ve beat him up.”
He added: “You didn’t cross your teacher in those days, that’s how it was.”
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On the minibus home Mr Brown said he was sitting behind Talbot and noticed that he was looking at a pornographic magazine with another pupil.
Later in school, Mr Brown said he stopped listening and failed Talbot’s biology class.
“I got a U - ungradeable - I didn’t listen,” he said.
“I had no respect for him.”
Questioned by defence lawyer Alan Gravelle, Mr Brown said he left school before Talbot began to appear on TV but was aware of his career because “he was on the TV every night”.
Asked why he had not raised the incident with authorities previously, Mr Brown said: “Every time I saw him on TV I told people this story.
“I’ve told hundreds of people the same as I’m telling you here.”
Mr Gravelle then asked if the witness had ever tried to tell Talbot’s TV bosses when he appeared on music shows with the Stone Roses.
Mr Brown said: “What, break off from my band and tell a camera man or something that the weatherman’s a nonce?
“It’s not realistic.”
Talbot is accused of carrying out the offences involving pupils aged 15-to-17 on trips in Scotland while he was employed as a school teacher.
He faces eight charges of indecent assault between January 1978 and November 1981 and one of lewd, indecent and libidinous behaviour in February 1978.
Six of the incidents are alleged to have happened on camping trips in Moffat, Dumfries and Galloway, and three on boating trips on the Caledonian Canal in Inverness.
The trial, before Sheriff Nikola Stewart, continues.