£ 600 Intel Gaming PC

If no monitor, no OS and no peripherals / optical drives are required, you can try this:

PCPartPicker part list / Price breakdown by merchant

CPU: Intel Core i5-4460 3.2GHz Quad-Core Processor (£144.00 @ Novatech)
Motherboard: ASRock H97 PRO4 ATX LGA1150 Motherboard (£70.76 @ Scan.co.uk)
Memory: G.Skill Ares Series 8GB (2 x 4GB) DDR3-1600 Memory (£52.20 @ Kustom PCs)
Storage: Crucial MX100 128GB 2.5" Solid State Drive (£53.15 @ Ebuyer)
Storage: Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive (£42.95 @ CCL Computers)
Video Card: PowerColor Radeon R9 280 3GB TurboDuo Video Card (£154.75 @ More Computers)
Case: Corsair SPEC-03 Red ATX Mid Tower Case (£45.80 @ Aria PC)
Power Supply: XFX 550W 80+ Bronze Certified ATX Power Supply (£50.95 @ Amazon UK)
Total: £614.56
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2015-04-08 11:23 BST+0100
 
PCPartPicker part list / Price breakdown by merchant

CPU: Intel Core i3-4150 3.5GHz Dual-Core Processor ($103.99 @ SuperBiiz)
Motherboard: Asus H81M-E Micro ATX LGA1150 Motherboard ($53.99 @ SuperBiiz)
Memory: Kingston Fury Black Series 8GB (2 x 4GB) DDR3-1600 Memory ($62.99 @ Amazon)
Storage: Samsung 850 EVO-Series 120GB 2.5" Solid State Drive ($65.00 @ Amazon)
Storage: Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive ($44.99 @ Amazon)
Video Card: Gigabyte GeForce GTX 970 4GB Video Card ($321.98 @ Newegg)
Case: Corsair SPEC-03 Red ATX Mid Tower Case ($49.99 @ Newegg)
Power Supply: XFX 550W 80+ Bronze Certified ATX Power Supply ($44.99 @ NCIX US)
Optical Drive: Samsung SH-224DB/BEBE DVD/CD Writer ($14.98 @ OutletPC)
Operating System: Microsoft Windows 8.1 (OEM) (64-bit) ($87.89 @ OutletPC)
Monitor: Samsung S24D300H 60Hz 24.0" Monitor ($149.99 @ Newegg)
Total: $1000.78
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2015-04-08 06:32 EDT-0400

total 1k $ od 669 pounds

if you dont include the monitor and OS ..then you can repalce the i3 with i5 4440 and the MOBO with H 87 Mobo
 


Pre-builts like these are a bad choice if the OP is even halfway capable of assembling his own rig. Both of these only have good CPUs, and the rest is completely unbalanced. Horrible power supply quality, using only integrated graphics for gaming, no SSD, and I cannot even find out do they have a regular HDD at all.

 
PCPartPicker part list / Price breakdown by merchant

CPU: Intel Core i5-4590 3.3GHz Quad-Core Processor (£155.26 @ Ebuyer)
Motherboard: ASRock H97 Anniversary ATX LGA1150 Motherboard (£61.03 @ Amazon UK)
Memory: G.Skill Ripjaws X Series 8GB (2 x 4GB) DDR3-1600 Memory (£50.77 @ Amazon UK)
Storage: Seagate Barracuda 1TB 3.5" 7200RPM Internal Hard Drive (£38.34 @ Aria PC)
Video Card: Zotac GeForce GTX 970 4GB Video Card (£255.00 @ Aria PC)
Case: Thermaltake Versa H22 ATX Mid Tower Case (£27.86 @ CCL Computers)
Power Supply: Antec Neo Eco 520W 80+ Bronze Certified ATX Power Supply (£37.32 @ Scan.co.uk)
Total: £625.58
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2015-04-08 12:05 BST+0100

or

PCPartPicker part list / Price breakdown by merchant

CPU: Intel Core i5-4590 3.3GHz Quad-Core Processor (£155.26 @ Ebuyer)
Motherboard: ASRock H97 Anniversary ATX LGA1150 Motherboard (£61.03 @ Amazon UK)
Memory: G.Skill Ripjaws X Series 8GB (2 x 4GB) DDR3-1600 Memory (£50.77 @ Amazon UK)
Storage: Seagate Barracuda 1TB 3.5" 7200RPM Internal Hard Drive (£38.34 @ Aria PC)
Video Card: MSI GeForce GTX 960 2GB Video Card (£159.98 @ Novatech)
Case: Thermaltake Versa H22 ATX Mid Tower Case (£27.86 @ CCL Computers)
Power Supply: Antec Neo Eco 520W 80+ Bronze Certified ATX Power Supply (£37.32 @ Scan.co.uk)
Total: £530.56
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2015-04-08 12:13 BST+0100

 

Agreed. Building your own computer leaves you with MORE MONEY and also leaves you with BETTER COMPONENTS in the long run!
 
Ok so there are different choices between your builds.One with an i3 and GTX 970 other with an i5 and weaker gpu.Which ones would you pick?I can't stretch my budget as I'm selling my AMD pc and this is what I will have to spend after it's sold.I also forgot to add that I have a monitor and Windows 8.1.