I was caught up in this - had an advance ticket for the 21:05 Waterloo-Sway.
Arrived at Waterloo about 20:15 (having travelled up from Barcelona since 09:25 local time, so rather tired).
Already knew there were problems and the 21:05 was cancelled, so headed for the ticket office, had my advance endorsed, and started looking for the first thing I could get. This was a very late running 19:35 which got me to Brockenhurst about 22:00 IIRC but was then fast to Bournemouth.
It looked as though there were no stoppers for a long while. Had a word with guard, who 'phoned control but said they wouldn't allow any additional stops as they were so late already.
So got off at Brock hopeful they might be laying on a taxi or two to replace the stoppers. But no staff, no reply from help points, and very cold! The 20:35 from Waterloo went through about 22:10, I asked the guard if she would be making any additional stops, but no.
So I gave up and got a taxi. I think the final train to Sway (22:05 from Waterloo) did stop there very late at about 00:30 though, but probably £10 for the taxi was better than spending 2 hours freezing on the platform at Brock.
Delay Repay claim in of course (I've attached the taxi receipt too, but don't know if they will take any notice of that.) The only slightly vexing part of the story was that when they were running two fasts (19:35 and 20:35) within about 10 minutes of each other, and no stoppers, it might have been nice if the second had had extra stops added.
(and that after travelling well over 1000km by train in a day, it's the last few miles that caused all the problems)