I need a high performance gaming tower?

I have a very small budget of only £350. I play minecraft and total war games. I also make mods which requires programs, so I also need the computer to be able to support allot of programs lag-free.

So you expect to get a high performance gaming PC for 350 British pounds? LOL!

It's a small budget, but nothing is impossible…
See what you can recuperate from an old computer so you don't need to buy for example a PSU or a case for that matter, same goes for monitor keyboard, mouse, etc.
If you could stick with mainboard/cpu/memory alone, you could really get something decent. Check pcpartpicker.com to find the cheapest dealers for your parts.

For example:
Mainboard: http://uk.pcpartpicker.com/part/gigabyte-motherboard-gab85hd3
CPU: http://uk.pcpartpicker.com/part/intel-cpu-bx80646i54670k
Memory: http://uk.pcpartpicker.com/part/corsair-memory-cml8gx3m2a1600c9

You can use the internal HD4600 graphics and save yourself some money on a GPU! This is a total of £298 and you have yourself a very nice computer. The CPU is on the high-end and the K model means you can still overclock it.