Sodium hypochlorite (about £12 for a huge drum) from farm suppliers will clean concrete easily.
Dilute 1:3 in water and sprinkle on damp slabs with watering can. Wear gloves and old clothes/shoes, keep pets away, as it is basically the solution farmers use to clean milking sheds and is an irrritant.
Wait about 20 minutes, have a cup of tea, then hose off.
If very grubby, or if you're feeling energetic, scrub over with a deck scrubber while waitig for it to work. This works much better than any patio cleaner I have ever bought. Also cleans drains.