My garden furniture was out all last summer in the rain. I tried some off the shelf products but they don't seem to work. The black discolouration is very bad.
Usually bleach and water will work. If not, Home depot carries a product called ZEP mold and stain remover. That stuff works great on the plastic funiture I clean at a beach house. Its stronger than bleach. It will even take black mold off siding with out damaging it. I also used it on wood too.
There a several products out there for this but the key item is bleach.So dilute some with hot water and spray on or wipe use scrub brush on it and let it sit .You can use tilex or any of those kitchen and bath product but if you have alot to clean the bleach is more cost effective.Make sure to rise with water when done.
Assuming it's wood, wet a small inconspicuous spot and apply a solution of 1cup of household bleach to a quart of water to see how strong a solution you need. Let it soak for at least 15 minutes and then scrub with dishwash liquid soap and water. Do this on a sunny day.
jeys fluid is really good, you can buy some that is for patios and patio furniture! i scrubbed mine with this , then hosed it down and now as good as new, but it from wilkinson's or tesco in cleaning isle.
Good luck with the clenaing!