Separates will usually give you better sound quality than a mini/micro system, but building a separates system of amp, CD player and speakers on your £300 budget will be tight.
Cambridge Audio's Azur 340C CD player is a terrific bargain at £150, and you could match it with Cambridge's Azur 340A SE amp (£180) and Tannoy's Mercury F1 Custom speakers (£110). But this will obviously bust your budget at £440.
The alternative is an all-in-one system. The best we've tested is Onkyo's CS-515DAB with speakers, which sounds almost as good as separates and is bang on your budget at £300 (or £230 if you buy it without speakers and add your own). It also has a built-in DAB tuner.