The thread seems to be diverging from the original question, which concerned an initial call to London Control (i.e the Area Control Centre, or enroute).
The answer to that question is indeed in the UK AIP, namely:
GEN 1.1.1
The initial call changing radio frequency shall contain only the aircraft identification and flight level. Any subsequent report shall contain aircraft identification, position and time except as provided for in respect of helicopter operations in the areas specified in paragraph 1.1 (d) above.
Note: 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.
... and for traffic departing on SIDs, the initial call requirements are contained within the relevant aerodrome SID chart, e.g.
AD 2-EGLL-6-1 London Heathrow Compton 3F SID Note 4
Callsign for RTF frequency used when instructed after take-off 'London Control'. Report callsign, SID designator, current altitude and cleared altitude on first contact with 'London Control'.
Discussions about the requirements on transfer to Approach units or Directors, etc, can be answered here, but are not what was originally being discussed.