The PM would very likely be William Whitelaw who was de facto deputy PM at the time and was trusted by the whole party as a safe pair of hands. This would create the constitutional curiosity of a Prime Minister in the House of Lords which would normally be inconceivable but as parliament isn't sitting during conference season Whitelaw would probably be acceptable to steady the boat while the Conservative party organises a snap leadership election in order to get a permanent PM in place before parliament sits. As to who wins that - no idea, but my gut wants to say Heseltine who certainly has the ambition and as Secretary of State for Defence will be in a good position to make crowd please blood and thunder speeches denouncing the IRA.