I wasn't there for the GCA, but I was in the UK in 1988 when they banned all semiauto rifles except .22 rimfires.
At the time, speaking out against the ban was politically equivalent to condoning mass killings. There was no question on the general public's mind that anyone would want to own such a rifle unless they were planning on going on a rampage.
It was all over the news, and the media wanted them banned, so they demonized gun owners.
There was no dissent among the political parties, so it was impossible to vote for a pro gun party because there was no such thing.
The media controlled the situation 100%.
Of course, in those days the media had 100% control over the news that the public had access to.
Britain had already outlawed firearms for self defense long before, and we had no equivalent of the Second Amendment.
We also had no real equivalent to the NRA. Gun advocacy in the UK was splintered, and the attitude was a 'ban their guns as long as we get to keep ours' mentality.
Here today in America, things are different.
We have the Second Amendment, the NRA, lots of pro-gun politicians, a more gun-friendly public, and of course the internet.