Bristol farmers market. Corn Street . Every Wednesday 9.30 - 2.30 has good veg producers. Also regular organic/slow food market, and the weekend of the 2nd/3rd Sept has the organic food fair in Bristol so get to that and find a good veg box scheme that will deliver proper food to you.
Try the vine ripened ones in supermarkets - they are more expensive but a lot better than the cheap ones. Otherwise check our farmers markets etc for home grown produce which you just won't beat