Ideally you would want to upgrade your CPU AND GPU, The fx 6300, is quite old and will bottleneck cards like the rx 480. But you can't upgrade both with just £200.
You have 2 choices. Either you upgrade to an i5 6500 with a cheap H110 motherboard. That will cost you about £220-230.
Or you get an rx 480 and live with the bottleneck until you can upgrade your CPU. The cheapest 480 that's in stock right now is the powercolor 8gb 480 for £229.
If you upgrade your GPU, you would see a big jump in performance, as opposed to upgrading your CPU, in which case the gains would be minimal if any at all. However you wouldn't have to worry about upgrading your CPU for the next couple of years. With the GPU it wouldn't take long for the AMD or Nvidia to bring out a gpu that will give you the same performance for less than 2/3 of the price.
I personally would go for an rx 480 to get an imidiate impact on my performance. But If you are someone that doesn't like upgrading every 2 years, you might wanna consider an i5, since CPUs last longer than GPUs.
PS: Your PSU is fine