CDM got nothing to do with it - we are talking EOBT here - look in the UK AIP Enroute section which clearly states the requirements, and points out nothing to do with ATC unless ATC are the cause of delay.
It's been regulation for probably 10 years plus that it's the aircraft operator/airline/handling agent (delete depending on your operation structure) to ensure that you EOBT is updated - the issue comes that airlines know they will never make the EOBT(plane not even arrived yet) but don't update it - the crew then call ATC when ready for push and rightfully so nowadays ATC tell them to get their operations(who you paying money to) to update it, issue is for years ATC used to fix it for you - but that can cause all sorts of issues - plus we often now employing someone to do that for you.
Form a network point of view and sector management and production of slots it's the EOBT that generating these restrictions - so in pre planning if from EOBT 10 aircraft are planned to depart and be in a sector at the same time this could result in some form of flow, when in reality 5 of those aircraft won't be departing then they just haven't updated their EOBT - so other aircraft are getting slots based on false data - so airlines that only update their EOBT at last minute generally buggering the system up for everyone else!