In DIY places, garden centres, etc, you can get some stuff called Patio Magic. You just dilute it and spread it on with a watering can. It kills the algae quite quickly, and your patio will smell like rotting seaweed on a beach for a few days. It then, as explained on the container, takes quite some time for the algae to flake off. I thought it wasn't going to work, but it did gradually do the trick for me.