Okay, I don't know much about Mining, especially for anything other than Bitcoins, can you be specific with the currency you're going to mine?
Anyway, I don't really think that case is gonna be great, for airflow especially. You want to look at something with lots of vents. And you'll probably want to get some better fans regardless, as stock fans (particularity on a £27 case), are a load of crap.
Knowing that you're mining, when you are, GPU usage (assuming that it uses GPU and not CPU) will be pinned at 100%
Points I want to make:
I would reccomend a 1080 over RX580 CF.
http://gpu.userbenchmark.com/Compare/AMD-RX-580-vs-Nvidia-GTX-1080/3923vs3603
The performance of the 1080 is quite a bit more than the 580, and obviously in CF there will be degradation as they dont scale perfectly. Check this article too https://linustechtips.com/main/topic/768301-rx-580-8gb-crossfire-vs-gtx-1080/
and these ones
http://cryptomining-blog.com/tag/rx-580-mining-performance/
http://cryptomining-blog.com/tag/gtx-1080-mining-performance/
Definitely new fans!
In a £27 case, not much money can be spent on fans.
Fans I use are Noctua fans, they go for about £15, consider that two of them is more than the price of your case and you'll see why the fans in that case are going to be a pile of s**t.
The case is also pretty bad for airflow, it has NO grills on the top or sides, it just has front and rear. I would suggest a better case.
Power Supply.
I would put in a better PSU. When mining, the GPU will be pinned at 100%, consuming lots of power, you most definitely want a more reliable and better efficiency PSU. When a PSU dies it can take a whole system with it, it will die much faster if it's at full load or close to full load for prolonged periods of time.
http://www.jonnyguru.com/
That is a link to a website with reviews of power supplies, they're very in depth, they are very well respected, just look for something good, most EVGA and Corsair PSU's are well rated, but they do cost more money.
Water Cooling!
It's great for a number of reasons, even if you just go for an AIO cooler. It looks amazing, it makes for a much quieter and cooler PC, meaning that you components will last longer because they don't get as hot, (even when mining). If you wanna know more, ask anyone or message me for some help.
Why mine with a PC??
I'm not very educated on mining, but I thought that it wasn't very economical to mine on a PC, maybe that's just Bitcoins. Problem with mining is that it kills hardware much faster because of the stress it puts on them, and GPU's just dont mine as fast as dedicated mining cards do. Check this video (although it is about bitcoins, again, insight on exactly what you want to mine would be useful).
https://www.youtube.com/watch?v=PEu6AH2e0bE