Intruder,
In UK airspace,(UK rules and regulations),irrelevant of your aircraft type, a maximum of 1500 ft rate of climb should be used when within 1500 ft of a cleared level.(obviously to avoid nuisance TA or worse).
If your SID first Hard altitude (at or below) is for example 4000 ft,it is prudent to use a mode that will reduce the climb rate in an airspace as congested as London TMA and therefore set 4000 ft in your MCP to avoid busting the SID level,when level at 4000 feet,set 5000 feet and wait for the appropriate waypoint to start the next climb.
The loss of comms scenario in the UK :
If failure occurs when the ACFT is following a notified departure procedure such as an SID and clearance to climb, or re-routing instructions have not been given, the procedure should be flown in accordance with the published lateral track and vertical profile, including any stepped climbs, until the last position, fix, or waypoint, published for the procedure, has been reached. Then, for that part of the period of 7 MIN that may remain, maintain the current speed and last assigned level or MSA, if this is higher.