Several years since I researched this one so it might have changed (but I doubt it!):
The UK AIP said you set QNH as soon as you are cleared to an altitude unless further flight level vacating reports are required and then set QNH after the last FL vacating report. The ICAO Pan-Ops said set QNH unless level flight above the TL is anticipated.
Obviously follow company SOPS but the short answer subject to those is set QNH as soon as cleared to an altitude. The hazards of not setting QNH (especially with QNH less than 1013 mb) from the pilot's point of view is that you might bust the MSA and/or have a CFIT!!