If you need a PC that is cheap but powerfull, skip out on the SSD, an SSD is an extra luxury you should only take if you got the money, but since you want something rather cheap I skipped out on it as you already have a HDD anyways... The CPU is also terrible and a cooler isn't needed unless you plan on overclocking... Your motherboard was "overkill" for the buget and 2x4GB isn't needed either, so I took 1x 8GB. The PSU is good, but I found one that's 5 pound cheaper and does the same job just as fine... Optical drives? No need to take a pricy one, so I got you this cheaper one... The case comes with a fan, so once again, without overclocking there won't be need for it...

This puts you with this, I also "upgraded" the GPu to a R9 380, although I do highly suggest you to wait for the new AMD RX 480 benchmarks, they promised/showed good stuff, but you can't be sure unless there are unbiased benchmarks

Important note here: You can not overclock your CPU with this build here, although intel made overclocking the non-K series not possible. Thus I got a motherboard that doesn't allow for overclocking either.

CPU: Intel Core i5-6500 3.2GHz Quad-Core Processor (£157.99 @ Amazon UK)
Motherboard: Asus H110M-A D3 Micro ATX LGA1151 Motherboard (£52.03 @ More Computers)
Memory: Kingston HyperX Fury Red 8GB (1 x 8GB) DDR3-1866 Memory (£19.99 @ Amazon UK)
Video Card: XFX Radeon R9 380 2GB Double Dissipation Video Card (£123.48 @ Ebuyer)
Case: NZXT Source 210 (Black) ATX Mid Tower Case (£34.98 @ Amazon UK)
Power Supply: Corsair Builder 500W 80+ Bronze Certified ATX Power Supply (£40.00 @ Amazon UK)
Optical Drive: Samsung SH-118CB/BEBE DVD/CD Drive (£8.75 @ Amazon UK)
Total: £437.22

However if you do want to overclock I made this:

CPU: Intel Core i5-4690K 3.5GHz Quad-Core Processor (£185.99 @ Amazon UK)
Motherboard: MSI Z97 PC MATE ATX LGA1150 Motherboard (£64.99 @ Amazon UK)
Memory: Kingston HyperX Fury Red 8GB (1 x 8GB) DDR3-1866 Memory (£19.99 @ Amazon UK)
Video Card: XFX Radeon R9 380 2GB Double Dissipation Video Card (£123.48 @ Ebuyer)
Case: NZXT Source 210 (Black) ATX Mid Tower Case (£34.98 @ Amazon UK)
Power Supply: Corsair Builder 500W 80+ Bronze Certified ATX Power Supply (£40.00 @ Amazon UK)
Optical Drive: Samsung SH-118CB/BEBE DVD/CD Drive (£8.75 @ Amazon UK)
Total: £478.18

Slightly more expensive, but allows for way easier upgrades in the future, as you can overclock this build without trouble, although you would have to add the price of a CPU cooler, but this can come later, even without overclock this CPU practically outperforms most AMD CPU's...

I hope I helped you a bit, keep looking for better builds as I'm not a pro either

EDIT: I screwed up the list thingies so here you have 2 direct links to the build pages:
1. http://uk.pcpartpicker.com/list/4RPkLD
2. http://uk.pcpartpicker.com/list/rnRt6X