Advantage spot-on works for my cat, you'll need to get it from the vet. There are two dosages: one for cats below 4kg and one for 4kg and above. You administer once a month.
While there, get a spray for your house and use exactly as the instructions tell you. This is to kill any eggs that may be waiting to hatch. This could be a cause of re-infestation.
Make sure your cat is wormed regularly with a medication from the vet. Not something from the pet shop or supermarket, not strong enough dosage to be really effective. We use Profender spot-on, there are three dosages available based on bodyweight, effective for roundworms and tapeworms. The life cycles of worms and fleas can be linked which is why it's important to keep up. This spot-on wormer is good for cats that are impossible to give tablets to. It's dosed once every three months.