The major reason for implementing this ban was to deny Sinn Fein and the IRA the ability to use the media for propaganda purposes.
The basic reasoning stemmed from the fact that the IRA was using violent, terroristic tactics in its bid to pull Northern Ireland away from the United Kingdom. Sinn Fein was the public arm of the IRA movement and would use the media as a means of justifying what the IRA was doing.
The major argument for implementing the ban is that the ban prevented terrorist apologists from using the media (paid for by UK taxpayer money) to justify the killing of British citizens. In a sense, this would be similar to a wartime situation. No one would have thought anything of denying Oswald Mosley the right to advocate the Nazi cause on the BBC during WWII. Therefore, there was no reason to feel that it was necessary to allow Sinn Fein to promote the IRA's actions in "The Troubles."