Here's an idea for a build, think it's pretty solid and you'll even get a ssd for your OS installation, which is a big plus in my opinion, because it removes the OS workload from the HDD which is used for your games.
PCPartPicker part list:
http://uk.pcpartpicker.com/p/3qpKO
CPU: Intel Core i5-4440 3.1GHz Quad-Core Processor (£127.19 @ Aria PC)
Motherboard: MSI H81M-P33 Micro ATX LGA1150 Motherboard (£31.85 @ Aria PC)
Memory: GeIL Enhance CORSA 8GB (2 x 4GB) DDR3-1333 Memory (£36.99 @ Amazon UK)
Storage: Sandisk 64GB 2.5" Solid State Disk (£35.51 @ Aria PC)
Storage: Seagate Barracuda 1TB 3.5" 7200RPM Internal Hard Drive (£34.80 @ Aria PC)
Video Card: Gigabyte Radeon R7 260X 1GB Video Card (£86.85 @ Amazon UK)
Case: Fractal Design Core 1000 MicroATX Mini Tower Case (£28.92 @ Scan.co.uk)
Power Supply: XFX 450W 80+ Bronze Certified ATX Power Supply (£20.00 @ Maplin Electronics)
Optical Drive: Samsung SH-224DB/BEBE DVD/CD Writer (£11.72 @ CCL Computers)
Total: £413.83
Should run most games at High/1080p (better than PS4's 720p/900p upscaling...). Compared to a PS4 this will also be upgradeable if needed later on. Instead of being stuck on almost* the same quality of graphics the next 7 years or so.
*Console games do get a bit prettier with time (for example compare GTA IV in the early PS3 days and GTA V in the late PS3 days.)