PC for League and Minecraft on a 250 quid budget?

My current laptop can't run Minecraft and barely scrapes League so i was wondering if it would be possible to buy something for 250 pounds that could do the job.

i found this but i don't know if its any good http://www.cclonline.com/product/101992/NoMfgCode/All-CCL-Desktops/CCL-Elite-Buzzard-III-Gaming-PC/CCL-EL-BUZ3/

That will work for both. I'd say save up though and get a dedicated graphics card…