Batting is a matter of 'timing' rather than brute force. Timing a ball isn't a mystery, but a skill anyone can improve - even if your name isn't David Gower.
Point your elbow at the bowler as he runs into bowl. This encourages you to play straight. You should aim to 'rock the baby' with your elbows as you drive the ball, rather than slogging across the line.
Pick your bat up high as the bowler prepares to bowl. A high, straight back lift allows you to generate bat speed as you hit the ball.
Begin the downswing of the bat much slower than you think you should. This stops you playing at the ball too early, makes you watch the ball longer and means that you're accelerating the bat through the ball as you hit it. Sloggers swing hard and early, meaning they hit the ball too early and too slowly, spooning catches in the air.
Lean into the ball as you hit it, so the whole weight of your body is transferred into the ball. Bend your front knee as you play the ball and point your toe in the direction that you want to hit it. Pointing your toe at the bowler, as 'golden age' batsmen did is still a good idea.
As the ball hits the bat, and not before, uncoil your wrists to add punch to the ball. This does not mean hitting everything to leg, you can throw your wrists to the off side as if you're playing a hockey shot.
When cutting or hooking the ball, make sure your arms are fully extended. A cramped shot creates a catch.
Hit every ball along the ground, except an attempted hook or straight drive for six.