I am no expert but what we are doing is a lower carb, higher fat diet rather than absolute low carb and high fat.
So our shopping each week consists more of less of the same things (we shop in Aldi and Lidl with the odd bit in sainsburys)
bag of beef mince or lamb mince
frozen spinach, frozen broccoli, frozen cauli, frozen carrot and swede mash
chopped toms
olives, plain and salted nuts
tomatoes, beetroot, sweetcorn, butter beans, plain haricot beans, lettuce,cue, mushrooms, peppers,celerycarrots,aubergine,courgette
feta cheese, strong cheddar
fizzy water
lemons and limes (slice a lime, put the slices in the glass, squeeze the rest of the lime into the glass, pour over the sparking water)
chicken breasts,
bags of lentils
fish fillets, prawns, smoked fish
houmous, olive oil
very high cocoa chocolate
strawberries, melon, peaches, apples, bananas, pineapple, tangerines.
eggs, milk, frankfurters, cream
this list is give or take what we already have in the house and what we fancy at the time, we dont buy all of this every single week
The reason we cant go low carb is because I eat between 7-10 full portions of fruit and veg per day. I will often have some sort of ragu with mince for breakfast, and salad for tea. We eat a lot of nuts. My OH is the one who is T2 diabetic and he doesnt eat too much fruit, not as much as me. However we are very partial to strawberries and cream. We eat a lot of curries and are really into tarka dal at the moment, hence the lentils. My OH also eats bags of ready cooked puy lentils.
Obviously if you are really sticking rigidly to low carb a lot of our shopping wouldnt be ok for you.