This is exactly what was happening to my car.
I've only had it since Dec 09, and it cam e with spanking Federal sporty tyres on it.... However they are utter cr@p. Really dangerous overtaking. It was getting to a point where I didn't want to boot it round country lanes because is was a bit too twitchy. And I have my Daughter in the back a lot of the time too, so safety is paramount.
It came to checking everything from tracking, ball joints, rod ends etc... and cr@p tyres was the cause. The difference is outstanding. Transformed the handling. The Federals used to pull the car to the left all the time and I thiught something was really wrong or bent on the suspension...
I went for the Michelin Pilot Exaltos.