It depends what is mean by 'benefit' in this question.
Of course, every route would benefit from 250km/h running in theory so long as the journey times are increased when taking into account accerleration time and stopping distances. To what extent they'd benefit in the confines of what is reasonable, is another question altogether. Let's say we remove economics (within reason) from the matter and focus only on effiency and journey time improvements. It is agreed somewhat that 125mph under the current infrastructure is the most efficient to operate at. Anything more would cost more, and result in mininimal improvements in journey times - with the potential to even create longer journey times if acceleration is poor and breaking requires greater distances.
If you were going by alignments, one could argue that in Scotland you could shave off around 5-15 mins in 250km+ running between Dunblane-Aberdeen (economics aside), and . And if you were going by true benefits, then look no further than what HS2 shaves off.
What truly suits 150km+ (155mph+) running isn't alignments, or high usage commuter belts in a 100 mile radius, but sheer non stop running distance alone. Plain and simple. If anyone needed an example, look at the journey time from Hong Kong to Beijing direct on a high speed train is on an average miles per hour basis. 8-9 hours on the train, 3 hours by plane, 1200 miles. That's the equivilant of a direct train from London to Tunisia roughly, in 8 bloody hours. The same journey time that gets you from London to Inverness (~500 miles) or there abouts. A journey that'd only be up to (at a guess) 30-45 minutes quicker if you were to fork out the investment to allow the speeding up running on the straighter sections under current stopping patterns.
Certainly makes one think, and puts the speed increase argument into perspective in a UK context.