You just have to be extra careful; it's quite easy over the course of the day for a few pence here and there to add up and make your til down.
Make sure you always count your float more than once to double check because that can sometimes be an issue (I've found my float £1 short several times at work, once or twice it's even been £5 up or down; sometimes people just don't concentrate when they make it up). Be careful checking what people give you, especially if they give you a lot of coins, and double check when you give change back (again, especially if it's a lot of coins-it's surprisingly easy to accidentally give someone an extra £1 or something if you're having to give them a whole handful of coins). If you can, count it back to them.
It might make you slower to begin with, but once your accuracy improves and you've had plenty of practice, you should get quicker.