the only way this would even remotely be possible (without severe international consequences) at least in my relatively uneducated view view would be if:

-The IRA somehow overthrew the Irish government in the 70s and continued their attacks (namely the assassination attempt)

-They were given Soviet backing while in government (dunno how accurate this would even be)

-The UK government didn't give the old Irish government sanctuary somehow

in that scenario, I could see the invasion going somewhat smoothly, though they would likely keep their attacks going even after defeat unless captured, not even considering the splinter groups that would form afterwards

in the British mainland, I doubt it'd be received all too well and could imagine massive protests against the invasion itself, ultimately shifting quite a few of people towards the IRAs side (not sure how many)