'For restricted Fruit and Vegetables a maximum combined weight of 2kg per person, unless accompanied by a phytosanitary certificate. ' From listed European and Mediterranean countries you are allowed a combined weight of 2kg per person.
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bread, but not sandwiches filled with meat or dairy products.
cakes without fresh cream.
biscuits.
chocolate and confectionery, but not those made with a lot of unprocessed dairy ingredients.
pasta and noodles, but not if mixed or filled with meat or meat products.
Food. You can carry cakes, fruit, vegetables, sandwiches and all solid foods in your hand baggage. However, foods in sauces or with a high liquid content (such as sauces, pastes, soups and stews) cannot come through security. The size of container must not exceed 100ml, regardless of the amount contained inside.
Solid food items (not liquids or gels) can be transported in either your carry-on or checked bags within the continental United States. Liquid or gel food items larger than 3.4 oz are not allowed in carry-on bags and should be placed in your checked bags if possible.
Since olive oil is classified as a condiment derived from a vegetable, it does not fall into any of these major inadmissible categories; therefore, it is a safe assumption that the transportation of olive oil for personal and private consumption is accepted in your country.
For goods over the £1,500 threshold and restricted and excise goods, and goods over 1,000kg you will need to make a full customs declaration either by yourself or through an agent.