A list of foods that you CAN eat:
Any fresh/unprocessed meat and fish. (Anything processed, like crab sticks or pre-prepared burgers are likely to have carbs - always check the back of the packet)
Processed meats/fish - bacon, ham, smoked salmon, etc - in moderation (not just because they have carbs but also because they often contain artificial ingredients, which we are also trying to avoid)
Eggs - no limit on these
Veg/salad from the allowed veg list (and focusing on those that are 3g carbs per 100g or less)
Lemon/limes - you can use a little juice in marinades/dressings - just don't go mad and use a bucket-load.
Frozen veg can be brilliant and is often surprisingly good - whole leaf spinach is especially good; cauliflower and broccoli are good standbys.
Tinned fish like tuna (if you're buying things like sardines/pilchards/mackerel in sauces, check the carb count first)
Tinned tomatoes - for soups/sauces; although they are quite carby, a little can go a long way. Sainsbury's Basics chopped tomatoes in a carton are lower in carbs
Olive oil for salad dressings (ideally you shouldn't cook with olive oil but should use something like coconut oil instead - but coconut oil is very expensive, so this one is up to you)
Sesame oil for stir fries and marinades
Vinegar for salad dressings - not balsamic vinegar, which is very high in carbs, compared with ordinary vinegar which is zero carbs
Soy sauce - for marinades or adding to stir fries, but beware it does contain carbs - check the labels first
Mayonnaise - again, check the labels as the carb counts vary tremendously (and always full fat)
Butter - as much as you like for either cooking or putting on veg
Cheese/cream - in moderation; dairy can stall some people so go easy on this until you know if it affects you or not
Yoghurt tends to be better tolerated - always, always, always full fat though and always plain! (Vanilla extract in yoghurt is lovely - Waitrose make one which is sugar-free)
Olives - these are very low in carbs and make a useful snack as well as an addition to salads/sauces
Water. If you find still/tap water boring, then sparkling water is fine. You should be aiming to drink at least two litres of water a day.
The moral of this story - if it's packaged food or processed in any way - *always check the label for the carb count.