Although I refer glibly to 'the system' and assume that there is some form of common repository of flight plan data accessible to ATC units
No - fraid not. Flight plans are only addressed to the relevant units on the address list. (in the case of VFR's / IFR's outside CAS aerodrome of departure and destination, plus anyone else you may have added). If you're not on the address list you don't get a copy. The only places which can do Flight Plan interrogation are the two centre's (Scottish & London) plus (I'm guessing) the Flight Plan reception units.
There is another way to see if flight plans are 'in the system', by acccessing the Eurocontrol/IFPS website and being a registered customer. Most ATC units however don't subscribe to this - there's really no point.