I'm a gardener and the absolute best way is to steam cleam them. You can pay someone to do this but it would probably cost about £15 per hour but dont underestimate how long it takes. Alternatively, if you feel it is worth investing in a pressure cleaner you can get one for about £70. It does make an absolutely remarkable difference but the key is to bleach the patio after pressure cleaning. You need industrial bleach about 5% strength (supermarket bleaches are about 1.5%) and this will lift the patio by another 50%. Leave the bleach on for half an hour to an hour then rinse off. The patio will look like new. Pressure cleaners are also brilliant at bringing up moss ridden sun damaged wooden patio furniture as new.