I'm sorry to say but, for a good Battlefield 4 experience, you'll need to spend more than £350. The graphics card needed for good game play will cost you around £150 - and that's before you've bought case, motherboard, memory, disk drives, power supply, operating system, screen, keyboard, mouse and so on. Had you thought of buying secondhand from e.g. eBay?
Surface Pro 5 News - release date, UK price, features, specs