Bringing food items into the UK (from Chile)

You can read the UK government's rules on bringing in food items here:

https://www.gov.uk/guidance/personal-food-plant-and-animal-product-imports

The important bit looks like this:

From non-EU countries the following items are banned:

• all meat and meat products
• all milk and dairy products
• potatoes

From non-EU countries the following items are restricted:

• fruit and vegetables - no more than 2kg total weight combined per person travelling bivalves (live), egg products, eggs and honey
• fish, bivalves (dead) and fish/fishery products - no more than 20kg total weight (fish must be gutted if fresh, or processed, ie cooked, cured, dried or smoked) 2kg total weight combined per person - certain fruits and vegetables

So most of what you mention should be all right, although if they contain considerable amounts of fresh dairy it could be an issue. Note that a later part of the page mentions exceptions to the above:

*Confectionery, chocolate or cakes (including Christmas cake, Simnel cake or cakes containing nuts) are permitted from any country as long as they are for your personal consumption and do not contain fresh cream or high levels of dairy products. Confectionery that contain high levels of dairy products include Burfi, Gulab Jaman, Halwah or Halva, Ras Malai, RasGullah, Ladoos, and Chum Chum. Information on importing nuts can be found on the Trade information: nuts (Food Standards Agency) (PDF, 164KB, 2 pages) .

As for declaring - you'll probably have to go through customs wherever you collect your bags first - which will be the UK if you have a ticket right through, or Italy if you have two separate tickets (probably).

Unlike the US, there is no declaration necessary - either you are travelling within the rules, in which case there is no need to declare, or you are bringing things which are not allowed, whether you declare them or not. "Declaring" to EU customs is either:a) for things you need to pay tax (typically VAT) on, or b) for things you aren't sure about and would rather a customs offical look at.