The song "Lola" by The Kinks was banned by the BBC not because of its subject matter about a cross-dresser or transgender woman, but because it originally mentioned the brand name "Coca-Cola" in the lyrics. The BBC had a strict policy against product placement and advertising on its airwaves, so the mention of Coca-Cola was seen as a form of advertising and led to the song being banned from radio play. The Kinks had to re-record the song to change the lyric from "Coca-Cola" to "Cherry Cola" to comply with the BBC's rules. After this change, the song was allowed to be played and became a significant hit.
Although the song "Lola" was notable for addressing themes involving a transgender woman, which was considered edgy for the time, the reason for the initial ban was strictly due to the product placement issue and not the song's gender or sexual identity content.