The output energy required for running at a constant speed of 250mph over a certain distance is four times that for running at 125mph (asuming same aerodynamics) because drag force (which at those speeds would be the dominant resistance force that the output power is equal to) squares with speed and work done is force integrated by displacement. There is also the fact that the energy required to accelerate to full speed will be four times as high because kinetic energy also squares with speed.
I am not saying that you are wrong to say that High Speed rail is cheaper, I am just not sure that you have proof that it is the case.
We also have to consider the probability of energy prices increasing in the future as certain fossil fuels run out and more strict global warming related regulations might be brought in.
Remember that while power demand will go up by four times, to a first approximation the
energy demand will only double because while you have to provide four times the power, you only have to do it for half as long to reach your destination.
And I base my projections on 320kph as I expect 360kph running to be abandoned rapidly if it is not done so before the service begins.
Energy costs are also very minor for passenger trains compared to other costs. Especially as with such short travel times on the captive sets as 90 minutes (on the Leeds-London journey which will be the longest really) the ratio of first class to standard seats could be expected to shift drastically compared to current practice on the routes concerned.
(My 1350 seat 400m Duplex type job projection assumes 1108 standard class and 244 first class seats, with one 18m trailer catering vehicle containing no assigned seats).
For reference I estimate the entire energy bill for such a set on a round trip from London to Birmingham to be something on order of £800, so about sixty
pence per seat for a round trip.