It should be noted that mould can stain your timber deck, so leaving mould growth (normally in the form of a black stain) to set in will mean that it is harder to remove.
For those that were perhaps a little lax in their cleaning efforts, there are some solutions.
Good old household bleach in a 1:5 bleach water ratio is an effective, cheap option, although relatively toxic. Leave the solution on the deck area for no more than 15mins. And be sure to rinse thoroughly with clean water and a stiff brush.
Be aware that bleach can burn or damage skin, and surrounding plants. Take care and follow the instructions on the can.
Another type of deck claners use persistent anti fungal chemicals such as benzalkonium chloride or quaternary ammonium compound. These chemicals will remove or destroy many fungi and moulds. Apply and leave for some time. Often a follow up scrub/rinse will assist and cleaning up your deck. These chemicals can be damaging to freshwater marine life, so be aware of this. While as not as dangerous as bleach, follow the precautions on the packaging.
One of the more eco options or deck cleaning is sodium percarbonate, which is usually supplied in a white powder. Dissolve the white powder in warm water, and the formula will release oxygen. Scarily it is indeed the oxygen that attacks the mould,slime and fungi, cleaning the deck quite thoroughly. Try Abodo's Rejuvenator.
When the going gets tough, Oxalic acid is an option. Oxalic acid can remove stains effectively, and in some cases actually remove a few layers of the wood itself. Oxalic acid can damage plants and can irritate skin. Be careful.
And PLEASE, do not waterblast your deck, no matter what the manufacturers of overpriced cleaning gadgets tell you.
Powerful jets of water can damage your decking timber, lifting timber fibres. The net result could be a “fluffy” deck, or even one that is more prone to mould and dirty build up than it was to start. A standard hose pressure and a stiff brush/broom is recommended.