Interesting subject, as others have noted, it depends how one defines this, especially as the OP's "other uses" covers a wide area.
After the last scheduled passenger service, the 21.25 Preston to Liverpool on 3 August hauled by 45318, at some time on August 4, Black 5 45212 shunted/heated? sleeper carriages in the bay platform at Preston (there's a photo of this on Flickr, but it clearly appears to be in the day time - was it early evening on August 4?). There is also photographic evidence that 48519 worked, shunting engineer's wagons at Rose Grove goods yard on the same day:
https://www.flickr.com/photos/90397953@N02/albums/72157632127202598
Then if you go down the road of "other uses", etc., British Rail ran a steam railtour on 11 August 1968, that is to mean, I think, that it was with their own motive power, rather than as later, privately owned steam running on BR metals with BR stock.
Obviously the very interesting info provided upthread extends "BR use" to much later dates.