Well, take away the assassination of the British Prime Minister on British soil and you take away a lot of the reason for the hard-line British stance on Northern Ireland. I mean, the war was fairly unpopular among certain segents of the British population at times IOTL, especially among the left—and that was
with the massive boost in support of complete suppression of the IRA following the murder of Thatcher by IRA terrorists. Without it, I actually think Britain may have given up on Northern Ireland, despite what the IRA would do to everyone who opposed them if they took over the province; this was the era of British decline, there really wouldn't be the determination required to pull through the Troubles if not for the confidence in moral rectitude provided by the IRA animals demonstrating how barbarous they are.
I know, to imagine any TL where the IRA weren't stamped out and crushed is pretty dystopic, but I do think that's what would have happened. With that, relations between the UK and Southern Ireland might have been less utterly icy than OTL.
For all the sort of radicals who think Thatcher's weird brand of Reagan-style imported American "conservatism" (more like quasi-anarchism) could have somehow survived, though, I think they're gravely mistaken. The ideas that set it up in America, with the tradition of revolution and irrational hatred of perfectly useful government action, simply don't exist in Britain. Thatcher was basically the ideological linchpin of that movement; without her it falls. If she doesn't get assassinated, the rest of the Conservative Party won't
immediately go with "One Nation Conservatism" and basically reverse her crazy and destructive economic reforms, but (although it tends to be forgotten now, with all the stuff about Britain's first female Prime Minister, murdered by terrorist scum) Thatcher at the time of the assassination was actually really unpopular among a lot of people; she'd confront the next general election and probably lose, and then the Tories would go back to One Nation Conservatism.
{edit}
OOC: You need to provide a better historical context for people to work with. When did she die? Who killed her? Why did they kill her? Who else was killed? When during her premiership did it happen?
Haven't you heard of the attempt to kill Thatcher IOTL? That's what
Historyman 14 is referring to.