It is forbidden to bring milk and eggs into the EU, but what about (home-baked) cake containing milk and eggs? Is the cooking considered to make it safe?
Assuming that you wish to 'import' from outside of the EU...
tl;dr cakes are ok
The controlling reference for your question is COMMISSION REGULATION (EC) No 206/2009 of 5 March 2009 on the introduction into the Community of personal consignments of products of animal origin and amending Regulation (EC) No 136/2004 and an explanatory note is here http://eur-lex.europa.eu/LexUriServ/LexUriServ.do?uri=CELEX:32009R0206:EN:HTML
The regulation prohibits both milk and eggs in some forms. However Article 7 lists the exemptions...
Exempted animal products. The following products are exempted from the rules explained previously:
- bread, cakes, biscuits, chocolate and confectionery (including sweets) not mixed or filled with meat product,
- food supplements packaged for the final consumer,
- meat extracts and meat concentrates,
- olives stuffed with fish,
- pasta and noodles not mixed or filled with meat product,
- soup stocks and flavourings packaged for the final consumer,
- any other food product not containing any fresh or processed meat or dairy and with less than 50 % of processed egg or fishery products.
The UK (an EU signatory to the EU regulation) has this to say about it...
The following products are exempted from the rules:
- bread (but not sandwiches filled with meat or dairy products)
- cakes (but not if they contain fresh cream*), biscuits
- chocolate and confectionery (but not if the sweets are made with high levels of unprocessed dairy ingredients)*
- unfilled gelatine capsules
- food supplements packaged for the final consumer containing small amounts of an animal product (such as fish oil capsules) and those
including glucosamine, chondroitin or chitosan
- meat extracts in liquid or spreadable form (but not pate or meat concentrates eg stock cubes, gravy granules or flavouring sachets or
any that contain pieces of meat) olives stuffed with fish
- pasta and noodles, if processed or cooked (but not if mixed or filled with meat or meat products)
- soup, stocks and flavourings packaged for the final consumer containing meat extracts, meat concentrates, animal fats or fish
oils, powders or extracts (but not if pieces of meat/fish eg when
dissolved in water)
- any other food product not containing any fresh or processed meat or dairy and with less than 50% of processed egg or fishery products
Based upon these references, you would be allowed to bring a cake in to the EU from outside the EU as a personal consignment.