My suggestion as for cheapest PC:
Your Basket
MSI Radeon R7 250 OC 2048MB GDDR3 PCI-Express Graphics Card 62,99
Corsair Builder Series CX 500w Modular '80 Plus Bronze' Power Supply 49,99
AMD A6-6400K 3.90GHz (Socket FM2) APU Richland Dual Core Processor 47,99
Western Digital Caviar Green 1TB SATA 6Gb/s 64MB Cache - OEM 41,95
Asus A55BM-E AMD A55 Chipset (Socket FM2+) DDR3 Micro ATX 39,95
GeIL Black Dragon 4GB (1x4GB) DDR3 PC3-10666C9 1333MHz Single 31,99
BitFenix Neos ATX Tower White/Red 29,99
Samsung SH-118BB/BEBE SATA 18x DVD-ROM (Black) - OEM 12,95
Subtotal £317.80
£264.83 ex VAT
Now it's all about if you want red case, pink or black. Same pretty much for graphics card (which you said don't have to be, but I suggest you get at least cheapest one).