How can I upgrade a PC for gaming ?

what budget are you looking at, give me a range, and I can build you an awesome spec list.

I'd start with 3 items, a GeForce GTX 1060 6GB GPU [Or Graphics Card] and an SSD, something cheap and fast. I'm honestly very surprised that the PSU hasn't screwed you over yet. It seems like it is very cheaply made and very-very bad. I've included a new one to help with your upgrades. With some other specs on the PC, everything looks good. You got yourself a good CPU, a good amount of Hard Drive space, but I think you should do something to make the thread more organized [I'll leave a little copy-paste at the bottom for a little help. Also, how many GB of Ram is in your build?

I made this up for a little bit of upgrade with an SSD from OCZ and a better and stronger GPU from EVGA, as well as an EVGA 500W Power Supply to power your machine. I'm not aware of how many watts it takes to power your system, but I think that 500W should be enough and leave you with a little bit of upgrade space.

PCPartPicker part list / Price breakdown by merchant

Storage: OCZ TRION 150 240GB 2.5" Solid State Drive (£59.99 @ Amazon UK)
Video Card: EVGA GeForce GTX 1060 6GB 6GB SC GAMING Video Card (£253.98 @ Amazon UK)
Power Supply: EVGA 500W 80+ Bronze Certified ATX Power Supply (£44.99 @ Overclockers.co.uk)
Total: £358.96
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2016-11-16 02:17 GMT+0000

Your total price is coming in at around £360, I'm sorry for going over your budget, but I couldn't fit everything in the budget. I'm sorry about that ):

Now, to make the thread a bit cleaner and nicer, just copy and paste this into the "Update" section of the thread

CPU: Intel i5-4670k - 4.2 GHz
CPU Cooler: ThermalTake Contac21
Motherboard: Asus Z87-K
RAM: Crucial [Insert amount of GB Here] DDR3 1600 Mhz
Hard Drive: 2TB Sata 3
Case: Coolermaster K350
Optical Drive: Sony 24x DVD+/-RW
Power Supply: 750W CIT
GPU: Nvidia GTX660 2GB
Operating System: Windows 7 Premium 64-Bit
Internet Wireless LAN
Case Fans: 300Mbps MAX Green Case Fans

The reason I included this is because the thread was very hard to read without any commas and it wasn't really set up in a readable format from not having any commas. Not trying to be mean, but I included this to help with your upgrades

Although I am not a professional, this will have to be looked over by a couple great builders on this website that I have spoken to in the past over these forums, and I'll tag them to see their opinion.

@Chugalug_ @Hlsgsz