Try starting out in the same way that real life instructors teach performance driving. Separate your inputs. Brake in a straight line, turn wheel smoothly, feed in throttle, wide open at apex, unwind wheel as you approach apex.
Being smooth with your inputs is very important. As you get comfortable, you can start merging your inputs. You will even begin the concept of trail braking without conciously doing it.
Ultimately, your speed is governed by the way that you exit corners. If you dive into a hairpin turn and blow the entrance, your exit will suffer, and thus your straightaway speed falls. Enter slow, exit fast.
Just for kicks, try the UF1 at Aston Historic. That will teach you how to be smooth and the idea of slow in/fast out.