Just had a look in the 737 FCTM to provide a reference since requested here so there it goes:
Normally, set all maximum or hard altitude constraints in the MCP altitude window. The next altitude may be set when the restriction has been assured or further clearance has been received. This procedure provides altitude alerting and ensures compliance with altitude clearance limits
Ie:Hard altitude is AT or BELOW .(AT 4000,5000B...)
If you are given vectors,it is airmanship and CRM to confirm with the controller if restriction still applies.
In the UK as you know,when no restriction you will get the "climb NOW FL070"...