Answer by taking a quote from the following article:

Frankie Goes to Hollywood (FGTH) were a British band formed in Liverpool, England, in 1980. The group was fronted by Holly Johnson (vocals), with Paul Rutherford (vocals), Peter Gill (drums, percussion), Mark O'Toole (bass guitar), and Brian Nash (guitar). The group's 1983 debut single "Relax" was banned by the BBC in 1984 while at number six in the charts and subsequently topped the UK Singles Chart for five consecutive weeks, going on to enjoy prolonged chart success throughout that year and ultimately becoming the seventh best-selling UK single of all time. It also won the 1985 Brit Award for Best British Single.

"Relax" was released by ZTT in October 1983 and got a modicum of airplay, allowing it steady progress into the UK Top 40. Following a debut on the BBC's Top of the Pops on 5 January 1984 while at number 35, the single rose to number six the following week.  On 11 January 1984, BBC Radio 1 disc jockey Mike Read was playing the record on his show when he noticed the front cover design (by Yvonne Gilbert). Read apparently became outraged by the "overtly sexual" nature of both the record sleeve and the printed lyrics, which prompted him to remove the disc from the turntable live on air, branding it "obscene".  Two days later - almost three months after the single's initial release, and just eight days after the group's Top of the Pops appearance - the BBC banned the record from all its TV and radio outlets, with the exception of its Top 40 show. "Relax" immediately shot to Number One in the UK charts and stayed there for five weeks, during which time the BBC could not feature the nation's best-selling single on Top of the Pops.  The original video was directed by Bernard Rose and depicted a gay S&M parlour where the band members were admired by muscular leathermen, a bleached blonde drag queen, and a large-bodied man dressed as a Roman emperor. The video featured a scene where one of the band members wrestled a live tiger, to the admiration of the clubgoers, and ended where the "emperor" was so excited he shimmied out of his toga. Filmed in the unused East London theatre Wilton's Music Hall, it was promptly banned by both the BBC and MTV, resulting in the production of a substitute video directed by filmmaker Brian De Palma to coincide with the release of his film Body Double.  The BBC lifted its ban on "Relax" at the end of 1984 to allow the band to perform it on the Christmas edition of Top of the Pops (it had been, aside from Band Aid of which Holly Johnson was a participant, the biggest-selling single of the year).

WHat is an interesting fact about the video?
the BBC banned the record from all its TV and radio outlets,