You could build this computer for less than £150, I don't know how much you're paying but this won't cut it for smooth minecraft gaming. If money is your issue, go with an AMD machine, preferably a quad core since they're targeted towards budget builds with great performance per £.
Integrated graphics also are pretty bad with running minecraft. You definitely don't need anything like a 980/1070... But you could pick up a gtx 670 for under £100 on ebay. It's a very good value card and will definitely handle minecraft with ease.
