Official Singles Chart on 22/1/1984

There was not a blanket ban. Between Nov '83 (release date) and Jan 84' you could hear it on Radio 1 and other commercial radio stations. It was only when Mike Read (Radio 1 DJ) publicly condemned the lyrics that it was banned from BBC radio. By then the song had already been aired on TOTP. However you could still listen to it on the BBC's John Peel / Kid Jensen late evening radio shows. You could also continue to listen to it on commercial radio and tv stations such as Channel 4's 'The Tube'. By the end of 1984 the BBC had lifted the ban probably due to embarrassment as it, in part, lead to its increase in sales. It was even aired on the 1984 Xmas edition of TOTP and Radio 1's 1984 best selling singles of the year. During this period the only format available was the 7"/12" single as the release of the album 'Welcome To The Pleasuredome' wasn't released until Oct '84 thus assisting its sales and climb up the singles charts.

Banning a record can often lead to greater sales through its controversial nature - looking at the list of originally banned records from the BBC indicates the amount of commercial success a song can have -

https://en.wikipedia.org/wiki/List_of_songs_banned_by_the_BBC

One of the oddest banned songs was 'Landing of the Daleks' from The Earthlings, because it contained a section of morse code, repeatedly saying S.O.S. The BBC banned it because they feared it might cause confusion amongst the public who might think it was a real SOS call.