I had great problems geting a DEP signal sent for a homebriefing.com flightplan about 2 months ago.
That's a different issue.
For AFPEx, there's a clearly set out procedure. FISO contacts AFPEx helpdesk, and it's the AFPEx team that find the FPL and send the DEP to the appropriate addressees.
If you file a VFR FPL via another method, whether homebriefing or your friendly local ATC, neither London Info nor Heathrow FBU would easily know who you sent the FPL to, and therefore who to send the DEP message to, would they? IFR is easier as it just goes to IFPS.