Stepped Climb Proceedure

[oapilot]

Good morning ladies and gentlemen.

I have a question regarding stepped climbs as part of a SID which I encountered the other day for the first time in my inconsiderable experience.

Departing from a London aerodrome our clearance included "caution stepped climb proceedure", which was set out clearly on the departure plate. We briefed accordingly as to the altitudes we needed at various points in the departure. On handover to London Control, we were cleared to the next altitude on the SID, and all went smoothly.

I'm wondering now however if our thinking during the brief was correct, so would appreciate some clarification on the following.

Knowing how busy London can be at times, I'm presuming that had we been unable to establish contact with London before the next step up in the climb, as the SID shows the vertical profile expected, that we should follow the published SID and climb in accordance with that profile.

Also, if no further climb instruction is given on handover, as long as we are still flying the SID, would you expect us still to climb accordingly? I'm just mindful of how busy the airspace is, so would rather make an arse of myself on here, than up there!

Have a good day.

OAP