Simple no wind basic explanation.
Jet engines are most efficient at relatively high power settings.
Airframes have certain speeds which are most efficient.
to have the two happening at once usually requires the aircraft to be operating high - say FL300 to FL360.
So to keep it simple let's just say that aircraft get the most miles per gallon in the cruise.
Therefore the simple answer is that the most efficient way to fly a jet aircraft is to climb as quickly as possible to the cruise level and stay there as long as possible.
From this you will gather that in order to stay at cruise level as long as possible requires a steep descent. Therefore the most efficient possible end to a flight would be to remain at ideal cruise level until such a point that the throttles are closed and the steepest possible path followed to landing. Being a relatively clean aircraft, steep descents usually result in high speeds
In other words,
Steep dive throttles closed from cruise level to a point where the dive is made less shallow and the speed bleeds off in time for the aircraft to be stable and configured on the approach with eht power at the correct setting.
Good in theory. Impossible in UK airspace!!
In reality, the ideal speed is always dependent on the wind.
If the aircraft NATS are talking of are descending at 275Kt into a 275Kt headwind they are going to use all their fuel going nowhere. Flying at 300Kt will improve the situation somewhat depending on time available.
A tailwind may make a slower speed more efficient.
Basically, such a broad statement is only going to work on a ideal day in the specific aircraft with the specific loading and the specific C of G position and the ideal descent profile.
Do NATS expect ATCOs to worry about all that?
Finally having said all of the above, for many operators, the cost of fuel is often less than the cost of maintenance. Therefore spending a few extra pounds of fuel to fly faster and save engine life can save the operator lots of £s over time with a large fleet.
Put simply, if it was that simple lots of people would be out of a job and the cost index would be a thing of the past.