An M20 pilot cleared to intercept the final to Runway 13L at BFI; experienced an NMAC with A C-177 transiting the airport traffic area. Local controllers were distracted and failed to advise of the traffic in a timely fashion.

Narrative

Approaching final on a three mile left base for Runway 13L at BFI at 1;500 FT Tower issued traffic/wake turbulence advisory for traffic on final (about 4 NM) for Runway 13R. A few seconds later tower called a traffic advisory for us indicating traffic (a Cessna Cardinal) approaching at 10 o'clock. Traffic was visually spotted almost immediately at an estimated distance of about 500 FT horizontal same altitude approaching from left to right at about 90 degrees to our heading. The aircraft appeared 'stationary' indicating a collision course. I initiated immediate evasive action with a left turn (behind) the approaching aircraft. We passed about 300 FT apart with the aircraft off our right side.I called the Tower later and spoke with a Controller who said that he witnessed the event. He apologized and explained that the Controller had become 'saturated' and simply got behind. The Cessna Cardinal had apparently been cleared earlier to transit the area - but this information had not been relayed to us when we checked in to the Tower. He said that he; in fact; had been in the process of 'plugging in' to assist the Controller when the event occurred.