Worth checking what Titan ones Screwfix has on offer. Last time I looked the Titan one was a lot more powerful for the same money than a Karcher at the same price range, plus easy to use Screwfix warranty if needed.
There are obviously much better commercial options for more money.
You might want to spray the patio with some sodium hypochlorite first.
Yup, you can get a 25L drum from farm suppliers for about £20, can dilute as required. Much cheaper and very quickly effective compared to patio cleaners. Over psray will obviously bleach anything else.