Next time consider just buying benzalkonium chloride (BAC), its the same chemical as patio magic, but the last time I bought some it was less than a fifth of the cost. I mix it down from the supplied 50% to 2 to 2.5% which is also stronger than the 1:4 ratio of patio magic provides which I think used to be about 1.75%.
BAC takes a long time to work unlike sodium hypochlorite which is favoured by companies for patio/roof/wall cleaning as it works much faster. However the results with BAC last longer and it isn't damaging to most surfaces as its just a biocide not bleach like sodium hypochlorite. Over the course of a year I turned an awful looking block paving drive and a patio back to great condition from green and spotted. I now just treat both with BAC and sealer every two years.