Costco for bulk like potatoes and onions - excellent premium quality - occasionally buy their soft fruit -v. pricey, but Californian. Mushrooms & tomatoes too, but only when we can use a bulk buy.
A 20 minute drive to Kenyon Hall Farm - excellent farm shop - the asparagus is just coming in now. They do superb pick your own - the whole range of soft fruit, and they import a pallet of Italian produce every week. If you're anywhere near, it's worth a trip
http://www.kenyonhall.co.uk/
Pop into Bent's while you're in the area - if M&S did a garden centre, this is it
http://www.bents.co.uk/
We have a Tesco Local 2 minutes up the road in our little village, and we shop carefully for odds and ends.
Sorry, rambling again ...