B & Q sell a patio cleaner fluid which you add to a watering can, pour on the slabs and leave for about 15 minutes before washing off with a stiff broom. I did ours recently, taking advantage of a rain shower which left the patio wet, which is the state it should be in before you start treating it.
With a lot of elbow grease it has improved the situation but if your patio is very grimy it may need a second treatment.
I'm not a fan of pressure jets. They leave the slabs looking wonderful but the pressure removes all the pointing between the slabs and then you have a major repair job on your hands.