Oi! Leave Nankangs alone!
Back on topic though, for anyone that says they lost in on a round about or a similar incident, you can't blame it on the tyres (Unless they're bold) It's down to the driver pushing it too hard or not knowing the cars limits.
Yes tyres, as Stevo says, will improve the speed you can take a corner, but at the same time - If you're driving normally, budget tyres are NOT going to kill you unless you drive like an idiot.
Even if there bold or bald you can't blame tyres still the driver pushing a car beyond its limit
All modern tyres will stop in the stopping distance mentioned in the highway code and if you crash in to this 10% of arctic docwra mentions its not because your tyres are @*!# it because your a tailgater and sit way to close to the car in front and no expensive tires that will stop faster don't give you the right to sit closer