The Conservative party would elect a new prime Minister from their ranks, there would be a by-election and the world would continue. Government economic policy would alter with the newcomer but not hugely.
Does this POD mean the Poll Tax doesn't get introduced ? That was probably the very worst notion Thatcher had, and caused financial chaos for several decades...
Mostly likely more violence in NI as reprisals happen, the US gets serious about blocking funding to Republican groups, Ireland increases operations against IRA units in the Republic.