It's leaving Prudhoe after 5am that makes the first one off peak.
Sheffield-Derby is off peak after 0900.
To get round the problem that led to my original post (station staff refusing to sell tickets that I request), yesterday I made my usual journey but this time prebooked over the internet and collected TOD.
Imagine my surprise that it offered me an Off Peak Day Return Sheffield-Derby for the 0923 , consistent with Yorkie's understanding of the restriction.
All other times in the past, even with me intending to get this train, Sheffield staff have sold me the considerably more expensive Anytime Day Return.
I was told on the train (XC Newcastle to Reading) that my Off Peak was "Not valid because it's before 0930". I protested politely and thankfully had a printed copy of the itinerary. The guard - very friendly incidentally - used his portable ticket machine to check the restriction and was flabbergasted to learn that, sure enough, the restriction Shef-Derby was now 0900. He seemed horrified (he's probably hauled loads of people up for it wrongly!).
My point: TOC training of guards seems lacking - but can you blame them given the massive complexity of restrictions.
Real point: "Simplification" has been anything but. Guard agreed with this.