The flight plan cuts out handover phone calls to the next sector by the controller. They all get a printed strip (you hope - not always) and all they do is press a button, say that G-XXXX is FL 80 tracking to XXX for a Zone transit of XXX. They then hand you to the next freq. Job done.
But you assume that the relevant controller gets your FPL. It depends. If it's a CTR/CTA controlled from Swanwick, perhaps. But I wouldn't depend on somewhere like Brize getting a copy of your IFR FPL. I've never found that even the LATCC controllers had my details, so in practice it seems to make no difference to workload.