If you are using fraps/bandicam you'll probably want 2 HDD's, play from one and record to the other.
You also didn't reveal what the £500 budget was for specifically. If it's for the whole system, you won't get the components you're looking for. Windows itself takes up almost £100 of that budget.
Personally, I feel this would be the best option:
PCPartPicker part list /
Price breakdown by merchant
CPU: Intel Xeon E3-1230 V3 3.3GHz Quad-Core Processor (£176.39 @ Aria PC)
Motherboard: ASRock H97 PRO4 ATX LGA1150 Motherboard (£74.59 @ Overclockers.co.uk)
Memory: Corsair Vengeance 8GB (2 x 4GB) DDR3-1600 Memory (£55.34 @ Scan.co.uk)
Storage: Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive (£38.40 @ Aria PC)
Storage: Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive (£38.40 @ Aria PC)
Video Card: MSI Radeon R9 270X 2GB TWIN FROZR Video Card (£144.50 @ Ebuyer)
Case: Zalman Z11 Plus ATX Mid Tower Case (£44.90 @ Amazon UK)
Power Supply: EVGA SuperNOVA 650W 80+ Gold Certified Fully-Modular ATX Power Supply (£64.99 @ Amazon UK)
Optical Drive: Samsung SH-224DB/BEBE DVD/CD Writer (£11.51 @ Scan.co.uk)
Operating System: Microsoft Windows 8.1 (OEM) (64-bit) (£79.89 @ Amazon UK)
Total: £728.91
Prices include shipping, taxes, and discounts when available
Ignore the name Xeon, that CPU is an i7 4770 equivalent, it just doesn't have an integrated GPU that you wouldn't use anyway since you have a dedicated one. It's a hell of a lot cheaper.
However, this setup wouldn't allow you to overclock but it probably wouldn't be necessary anyway - a stock 4th gen i7 will beat an 8320 @ 5GHz, which is a huge overclock. To be able to overclock you'd have to change the motherboard to a Z series, and get an aftermarket CPU cooler and change the CPU to a 4770k/4790k - that's an extra ~£200 for little gain.
If you're set on overclocking an i5, here's another option:
PCPartPicker part list /
Price breakdown by merchant
CPU: Intel Core i5-4670K 3.4GHz Quad-Core Processor (£155.99 @ Aria PC)
CPU Cooler: Cooler Master Hyper 212 EVO 82.9 CFM Sleeve Bearing CPU Cooler (£24.76 @ Amazon UK)
Motherboard: MSI Z97-G45 Gaming ATX LGA1150 Motherboard (£105.13 @ CCL Computers)
Memory: Corsair Vengeance 8GB (2 x 4GB) DDR3-1600 Memory (£55.34 @ Scan.co.uk)
Storage: Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive (£38.40 @ Aria PC)
Storage: Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive (£38.40 @ Aria PC)
Video Card: MSI Radeon R9 270X 2GB TWIN FROZR Video Card (£144.50 @ Ebuyer)
Case: Zalman Z11 Plus ATX Mid Tower Case (£44.90 @ Amazon UK)
Power Supply: EVGA SuperNOVA 650W 80+ Gold Certified Fully-Modular ATX Power Supply (£64.99 @ Amazon UK)
Optical Drive: Samsung SH-224DB/BEBE DVD/CD Writer (£11.51 @ Scan.co.uk)
Operating System: Microsoft Windows 8.1 (OEM) (64-bit) (£79.89 @ Amazon UK)
Total: £763.81
Prices include shipping, taxes, and discounts when available
Now, you might hit 4.4GHz on this chip. I'd wait until the i5 4690k releases (25th of this month) and get that instead. I'd expect the Xeon build to livestream, edit and record better, this i5 build may be slightly better for plain gaming depending on the game - and by that maybe a 5 FPS boost at most. In livestreaming/recording I'd expect the Xeon to drop far less frames than the i5. Either would be sufficient though.
If you want a laptop style keyboard you'll want to look at a chiclet one.