Any factual info on the class 31s true top speed in optimal conditions, and what was the typical load limit in tonnes on a non graded route?
Let's skip the 20 mph and skin off rice puddings comments

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The early years of my commuting between the Fens and London included a lot of class 31 hauled trains as they frequently substituted for unavailable class 47s.
They have been recorded at 100+ when on the so-called 'Cambridge Beer Trains' or 'Cambridge and Garden Cities Buffet Express' to give the full title - i.e. the buffet-car equipped London King's Cross to Cambridge fast services.
This is consistent with my experience on the Peterborough commuter trains, which were usually 8 cars. With a class 31 the morning trains would usually be 5-10 minutes late by the last call at Hitchin or Stevenage. It was then de rigueur for the driver to try to get as near as possible to on time arrival at Kings Cross. Speeds in excess of 90mph on the descent from Potters Bar were commonplace, and the fastest I recorded was 97mph.
On the Liverpool Street line there was no similar opportunity for very high speed running. On the down line the gradient is gently uphill between Tottenham and Bishops Stortford and, in those days, the line speed was 80mph, apart from a 70mph restriction at Roydon. The standard Kings Lynn sets were 9 cars, and with a decent loco the driver would need to shut off for the 70mph Roydon restriction. On the up road, with gently falling gradients, it was difficult to exceed 80mph without getting signal checks because of the large number of level crossings on the route, so speed was usually held in check at 75-80mph.
A single 31 would sometimes be entrusted with load 12 or 13 on a summer Saturday service such as the Yarmouth - Newcastle.
In the 1960s and 1970s this was the standard East Anglian way of doing summer Saturday holiday trains, with speeds a bit over 60mph on level track. By the 1980s it was a bit more difficult to experience that except between Norwich and Yarmouth, where most trains would be hauled by single class 31s, irrespective of the number of cars.
Personally driven 31412 on a 4 coach tpo working and the speedo went off the clock (estimated 105). Field stages came in early and maintained a good supply of amp's. Had to slow it down with a diverging junction coming up. No complaints from the tpo crew which was good !
I suspect that a lot of the fastest running with class 31s was on trains not available to fare paying passengers. Various TPO trains were only 4 cars, and, back in the 1970s, the Western Region had premium parcels trains that were class 31s hauling 3 vans.
The passenger train that I can think of that came nearest to replicating this was a Fridays only St Pancras-Derby in the late 1980s that was 5 cars. Class 31s on this working are known to have exceeded 100mph on the descent from Ampthill to Bedford.
Finally, as the OP is from Barrow, it is worth mentioning the Manchester-Barrow Regional Railways trains of the early 1990s, where class 31s on 4 cars could hit 90mph between Preston and Lancaster.