I like the first Intel build except for the G440 CPU. For a few quid (or whatever currency) more, you could get G540 dual core Sandy Bridge and stay within your budget. From what I have read, G540 has the advantage for basic computing (better CPU), A4-3400 has the advantage for gaming (better GPU). Since poster is not gaming, I would go with Intel.
Here is a revised build with a Micro-Atx Mini-tower case.
PCPartPicker part list:
http://pcpartpicker.com/uk/p/zjaL
Price breakdown by merchant: http://pcpartpicker.com/uk/p/zjaL/by_merchant/
Benchmarks: http://pcpartpicker.com/uk/p/zjaL/benchmarks/
CPU: Intel Celeron G540 2.5GHz Dual-Core Processor (£31.80 @ Aria PC)
Motherboard: MSI H61M-P31 (G3) Micro ATX LGA1155 Motherboard (£31.93 @ Scan.co.uk)
Memory: Crucial 4GB (2 x 2GB) DDR3-1066 Memory (£17.51 @ Amazon UK)
Storage: Samsung Spinpoint M8 250GB 2.5" 5400RPM Internal Hard Drive (£35.00 @ Ebuyer)
Case: Fractal Design Core 1000 MicroATX Mini Tower Case (£31.12 @ Aria PC)
Power Supply: Corsair Builder 430W ATX12V Power Supply (£35.32 @ Scan.co.uk)
Optical Drive: Lite-On iHAS124-04 DVD/CD Writer (£12.98 @ Scan.co.uk)
Total: £195.66
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2013-01-24 14:21 GMT+0000)