While the power draw of the 6670 might not be massive and your psu should be rated high enough for it's use as it was listed earlier. With the quad code CPU and everything else in the machine you are probably running quite high on the wattage of the 300w psu, so for the longevity of your system and the current PSU I would indeed recommend getting a slightly beefier one.
I have a eMachines T5224 that just blew it's 300w while being used with a 4650 DDR3, it was sufficient to run things but eventually just ended up being too much to handle.
Unfortunately the good gaming PSU's tend to start at around 80 quid, however such things as:OCZ 500W PsuOCZ 600W Psu
Are within your pricerange and are partly modular.
The previously mentioned Antec EarthWatts series is a decent choice too at that price range.Antec EarthWatts 430W
And you might also consider: Antec Gamer 400W