Had a run of putting gigs on where bands split up more or less after playing (tbf they were in Mansfield) - komakino, kubichek, the strange death of liberal england, though not sure they were officially the last gigs.
Went to the last Hope Of The States show until the reformation, and was at the last Aereogramme show.
Cleft’s last ever gig at Arctangent is the only one I can think of, it was absolutely joyous.
DEVO, Slint & NOFX’s last ever shows*
*Until they all came back
Went to one of Adebisi Shank’s farewell shows, though they added a second date after I’d bought my ticket (it was originally supposed to just be an album launch), and they followed it with a Japanese tour they’d already booked before deciding to split, so not quite their last show. But close enough.
Closest is probably Low’s penultimate UK gig 
Saw Bitch Magnet when they reformed and played the Lexington. Not sure where that was in the order of the tour.
Low at that Primavera for me, one of their last 5 or so gigs it seems
Saw Mission of Burma on what turned out to be their final tour in 2016. Apparently their final show was in Berlin about a week after I saw them in Dublin, though they didn’t announce they were finished until about 4 years later.
I saw Dimebag’s final UK festival performance with Damage Plan.
The Second Hand Marching Band’s last gig up in Glasgow.
Can’t immediately think of any other last gigs.
I saw Crash of Rhinos on the last date of their September 2013 tour, they broke up at some point in 2014
I was at Colour’s last gig in Sept 2010. Saw them 3 times on the final tour earlier that summer
Saw the Youthmovies ‘farewell’ show in Oxford where the guitarist concussed himself with his guitar in the first song and then muddled quite badly through the rest of the set
(The scare quotes are cos they played a few reunion gigs a couple of years ago)
I was at Mark Linkous’ final UK appearance.
Fugazi’s penultimate gig, but I have no doubt multiple people were here at the last one.
The London one? If so same
Was at the 2nd to last ever Texas is the Reason show at the Hop and Grape.
Think there was another user who had a ticket and didn’t go. (Massive error, it was an amazing gig)
Last show of the Muncie Girls farewell tour last December
I saw Sparklehorse for the only time at Queen Elizabeth Hall in London in October 2006. Not sure if they played again after that, but would have been disappointed to miss them/him if so!
His final UK appearance was at the Daniel Johnston & Friends gigs (the other friends being Jad Fair, Norman Blake, James from Yo La Tengo and Scout Niblett). All of the friends played an individual 3 song set, then Daniel Johnston played a couple of songs unaccompanied and then they all came together as his backing band. It was a great gig and probably the best circumstances to see Daniel Johnston.