@Matt - thanks for the Moti recommendation.
I went to their Bristol shop (Whiteladies Road in Clifton,
website) and got fitted with some good running shoes - they do gait analysis, which means videoing you running on a treadmill and analysing how much your foot rotates, as well as seeing how you balance and whether your knee rotates inwards when you bend it.
They are incredibly friendly and knowledgeable - they eat and breathe running shoes but are very good at explaining exactly why a given shoe would work.
For example, it turns out Gore-Tex is a waste of time for running shoes because the water can get in through your socks (wet grass, splashes, rain, etc) and then can't get out via the Gore-Tex - whereas a shoe without Gore-Tex may get wet, but lets the water exit more easily as your feet warm up. So actually Gore-Tex makes your feet wetter for longer! Something I didn't realise until explained but it makes sense, and I almost got Gore-Tex shoes from another shop that didn't explain this - an £80 mistake avoided.
I'd recommend Moti to anyone near Bristol - they also have shops in Cardiff and Reading, and an online shop with a great return policy (you can return for up to 30 days). Allow at least 1 hour for gait analysis and try to go at a less busy time if you can.
They have a running group in Bristol, suitable for beginners, and understand the couch to 5K concept. I also saw a poster there for a 'running style clinic' where someone (possibly a partner of Moti's) watches how you run and advises on technique.