It's on the ATIS of LCY anyways not to climb above 3000 feet after departure.
On the departure I think it's sensible of the crews to level off at 3000 unless cleared otherwise. Normally we reach 3000 even before intercepting the LHR radial eastwards.
Watching the TCAS and reducing rate of climb when reaching 3000 helps as well. I normally keep it at or below 1000 ft/min in the terminal area.
When departing LCY I use V/S 1'000 ft/min for the step climbs unless in the DVR area when cleared to a higher level. This reduces the risk of TCAS triggers with opposite descending traffic. Inbound or outbound this greatly helps. The lower rate also gives more time to monitor.