I agree with most of what's been said, but I'm not sure that Wilson would benefit politically. The question is bound to be asked, why did the government fail to act to restore order in Ulster earlier, instead of waiting for foreign troops to intervene before doing anything serious?
I suppose it could be argued that the time was true of the Falklands in 1982 in OTL. The robustness and success of the military response caused a real sense of patriotism and a huge political bonus for Margaret Thatcher.
A successful repulse of the Irish incursion into Ulster would have seen similar, though on a smaller scale. At a time when the Wilson Government was coming back strongly against the Tories, I'm simply arguing the possibility that a small patriotic boost to Labour might have convinced Wilson to go to the country in late 1969 and to win , albeit with a reduced majority (30-40 seats).
No Labour leader had ever won three elections (Blair would in OTL of course) and the Party's would be his to command. The Tories had conversely not lost three times in succession since the introduction of universal suffrage and with Heath a two-time loser, I suspect he would have been forced out by the 1922 Committee in the spring of 1970.
Who wins a Conservative leadership election? Maudling would be the obvious favourite but runours of his relationship with Paulson were already circulating in Westminster. One possibility is to have Iain MacLeod become leader and die within three months making him one of the shortest-lived party leaders on record.
Quentin Hogg is arguably too old while Enoch Powell is a more likely contender as is Keith Joseph.
We could have the scenario of Iain MacLeod becoming leader in March 1970 and dying four months later to be succeeded by Reginald Maudling who is forced out by the Paulson scandal in 1972.