Here's what I've picked out for you at the same budget:
PCPartPicker part list /
Price breakdown by merchant
CPU: Intel Core i3-4160 3.6GHz Dual-Core Processor (£89.99 @ Novatech)
Motherboard: MSI H81M-P33 Micro ATX LGA1150 Motherboard (£35.42 @ CCL Computers)
Memory: Corsair Vengeance 4GB (1 x 4GB) DDR3-1600 Memory (£29.60 @ Scan.co.uk)
Storage: Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive (£34.45 @ Aria PC)
Video Card: PowerColor Radeon R9 270X 2GB TurboDuo Video Card (£122.16 @ More Computers)
Case: Aerocool DS Cube Red Edition Silent Cube MicroATX Mini Tower Case (£55.99 @ Aria PC)
Power Supply: Corsair CX 600W 80+ Bronze Certified Semi-Modular ATX Power Supply (£56.99 @ CCL Computers)
Optical Drive: Samsung SH-224DB/BEBE DVD/CD Writer (£10.50 @ CCL Computers)
Monitor: BenQ GL2023A 60Hz 19.5" Monitor (£65.11 @ Amazon UK)
Wireless Network Adapter: TRENDnet TEW-726EC 802.11a/b/g/n PCI-Express x1 Wi-Fi Adapter (£20.30 @ Dabs)
Speakers: Logitech Z213 2.1 Multimedia Speakers (£24.36)
OS: Windows 8.1 Upgrade (£46.95)
Total: £591.82
Prices include shipping, taxes, and discounts when available
CPU: I decided to go with something that's faster yet less expensive, but has a little more power draw. So I traded the i3 4130T for the i3 4160.
Motherboard: Same features as the Asus board, decent overclocker, and a few £ cheaper.
Memory: Faster and about the same price as the DDR3-1333, but should allow for a little more OC headroom.
Storage: Faster, same capacity, and less expensive than the HDD you selected.
Videocard: The R9 270x 2GB is possible by trimming some fat off the OS price. Kicks the GTX 750 Ti's ass.
Case: This is probably the most subjective item. It's really your choice, but you can actually shift about £20-30 toward your GPU if you select a less expensive/flashy case.
Powersupply: I went for something that's modular with a little more juice should you decide to upgrade to more power hungry components down the line.
Optical drive: Cheaper and same/better performance than the Asus drive.
OS: There are usually deals for OS's. I usually find these for $30-50 USD by purchasing the upgrade version. You don't even need a prior Windows install to use the upgrade.
Wireless NIC: Cheaper and same performance as the Asus NIC.
Speakers: Got rid of the Lenovo cans. These should put out a nice round sound for you music and games.
There's actually an even better rig already spec'd out on the partpicker front page, but it doesn't have all the OS, speakers, WiFi NIC, DVD/CD drive, and monitor goodies you were looking for:
http://uk.pcpartpicker.com/guide/gcT...l-gaming-build