I would recommend building your own computer... I built my own and it has 10GB RAM, 3.2GHz overclocked to 4.2GHz, A pretty high end GPU and it is running pretty well. If you want me to design a good PC for you, just PM me, I saw that you were looking to spend around £300, if you were to go for a pre-built computer, I would recommend spending a tenner over your budget and getting this:
http://www.cclonline.com/product/115.../CCL-BUS-ENT2/
If you absolutely HAVE to spend £300 or under, I would recommend this:
http://www.cclonline.com/product/857.../CCL-EDU-MID1/
I would go for the computer for £309.98 because it has a 1TB Hard drive, which is really essential for Video editing.
Both of these systems WILL run Minecraft at 60FPS Solid!
CCL Are a really trusted supplier, hat's where i bought all of the parts for my computer, and it is still running today. Just for a bit more insight on CCL, they have been around since before 2000, and everyone I know who have used CCL are extremely happy with the outcome