When changing frequency between any of the London Control, Scottish Control or Manchester Control Centres, pilots are required to state their callsign and Flight Level/Altitudes only (plus any other details when specifically instructed by ATC). When the aircraft is in level flight but cleared to another FL/ALT, both FL/ALT should be passed. Similarly, when the aircraft is not in level flight, the pilot should state the aircraft identification followed by the FL/ALT to which it is cleared only; it is not necessary to state passing FL/ALT in these circumstances.
We're not talking about changing frequencies from one area controller to another. CAP413 should be followed unless there is an explicit local instruction on an AIP chart not to.
On initial contact with an EN-ROUTE ATS UNIT, passing level should be given. I have already quoted the CAP413 reference for this in a previous post. Perhaps you consider Stansted Director to be an en-route ATS unit, which I find bizarre but stand to be corrected. Maybe someone qualified could come up with a precise definition of an en-route ATS unit. IMHO it's only those who control our FIRs, ie London, Scottish and Manchester.