On the E190 which is fully VNAV capable we always and only set the cleared altitude on MCP.
As a regular on LCY (EGLC) and LHR (EGLL) we are familiar with the step restrictions in the London area. Strict adherence to cleared levels and if not clearead otherwise the steps on the SID takes you quickly close to other traffic.
As a general rule:
Set initial "CLEARED" altitude and subsequent "CLEARED" altitudes on MCP. This feeds the mode S repeater and ATC knows that you have set what you are cleared to.
If not cleared otherwise adhere to the intermediate steps.
The clearance: "CLIMB NOW TO FL110" implies cancellation of the steps - maybe someone can add the link to the AIP U.K.
Our policy and also IMHO the best way is to have the aircraft fly in VNAV but only set cleared altitudes on MCP. We (pilots) do not know why ATC restricts us further or clears us beyond SID steps.