V is an angry, rueful reflection on Leeds-born Harrison's estrangement from his working class roots and the divisions that scarred society in the mid-1980s, from the miners' strike to racism on the football terraces.
The last time it was broadcast, in a film for Channel 4 in 1987, it was described by the Daily Mail as a "torrent of filth" in which "the crudest, most offensive word is used 17 times".
The Observer said it was "the most sexually explicit language ever heard on television".
Conservative MP Sir Gerald Howarth attempted to get the broadcast banned, tabling an Early Day Motion entitled "Television Obscenity" and accusing Channel 4 of trying to "assault the public [with] more effing and blinding".
He described Harrison as "another probable Bolshie seeking to impose his frustrations".
Sir Gerald, until recently a defence minister, now confesses he had not read the poem in full when he made these comments - and had not realised it was about the desecration of Harrison's parents' grave.
"I had read enough to get a flavour of it," he says.
But he says he has no regrets about calling for it to be banned.
"I have every sympathy for Tony Harrison and what happened to his parents' grave. But the increase in the common currency of that sort of language is more likely to result in profanities on people's graves."
Art is never an excuse for broadcasting profanities, he argues, and he believes there is simply no place for the "c-word" and the "f-word" on television and radio.
"I do understand Harrison's deep sense of anger and frustration but I still do believe that it does not excuse the language. I do believe that it completely undermines his own objectives because it enhances the respectability - and acceptability - of that language."