HEATHROW DIRECTOR:
If TCAS issues a TA regarding a target close to the approach track, my first action would be to look for it and ask tower for confirmation. If the tower (or APP) has no contact with the traffic and it was only mode A equipped I would think twice before leaving my altitude. At the place I meant, usually the VFR aircraft are mode C equipped, which makes identification a lot easier as well as evaluating the threat potential.
Simply continuing without seeing the target blindly trusting that nobody would dare to fly through the final track is not my idea of safety.