From my operational experience at EGCC, ATC can update the EOB time via the NAS computer system and thus keep the plan active in the UK system, however this does NOT update the actual flight plan via Brussels. The danger of doing this, from an air traffic point of view, is that if the flight plan is not updated via the CFMU then there is the possibility of a slot requirement at the later time when the aircraft actually becomes airbourne which in return may result in overloaded en-route sectors, etc. Or on the other hand, if the destination airfield as affected by severe delays or even closure, the flight would not be aware and will depart only to find themeselves holding indefinitely! And unfortunately, it's usually the poor ATSA's that get the agro when the sh*t hits the fan!
So delay messages really should be sent by the operating company to avoid any confusion, and the P times (EOBTs) only changed by ATC to avoid squawks dropping out of the system, prior to and IN CONJUCTION WITH A DELAY MESSAGE FROM THE COMPANY!