I didn't know the story but I googled "Cliff Richard's name on a pen" and that story came up.
I had to laugh at the quote: "In the UK there's a cheap kind of pen called a Biro pen...."
Does he not know that the pen is named after its Hungarian inventor, Lazlo Biro, and that's why it's known as a biro worldwide?!
Funnily enough, if you hadn't included the word 'name' in your search, it wouldn't have come up. Something I had tried on google when quickly checking it wasn't too easy a clue. That story had done the rounds at gigs some 15+ years ago, surprised the article is as late as last year. There have been other joke explanations by them over the years, so not entirely sure I fully believe it myself.
I remember telling a good friend about them whem they first started, saying you heard of this new band etc etc. And he said, what the hell's a clyro. Which made me think he knew what a biffy was. But I was too proud to ask.