Brake earlier!
Seriously, drifting is dirty big fun but it's extremely hard on tyres, and unless done skillfully is generally slower than 'grip' driving.
The secrets to grip driving:
- do all braking in a straight line
- follow the correct line through a corner
- ease in power gently so as to avoid wheel spin and over/understeer
Your procedure when approaching a corner should be:
- ensure you're on the outside of the track
- brake sufficiently to reduce speed to cornering speed
- turn in
- once past the apex start to feed in the power to accelerate away (I tend to be slow in fast out, so I personally accelerate before the apex).