If you shop with Tesco (and I think Sainsburys too) you can check nutritional content of most foods online which is very handy.. Particularly check the total carbohydrate content (which will include sugars), and avoid anything with high values. So stay away from all high carb, sugary, starchy foods, and any that are low fat as these are liable to contain more sugars.
You'll need to make your own choices about how much you're going to reduce high carb foods, which will help you create your shopping list. If you search the forum for Viv's modifed Atkins diet thread there's a good list of recommended foods for lower carb diets in that. But certainly include fresh green vegetables and salads, meat, fish. poultry, butter, olive oil, cream, full fat (Greek) yoghurt, cheese, eggs, avocados, olives, nuts, and berries.
Robbity