As of 1 January 2021 the United Kingdom is considered as a third country in terms of customs regulations. Special rules by the Withdrawal Agreement are applied to Northerm-Ireland.
Therefore the same EU customs rules are applied to passanger traffic like to other non-EU countries. Please bear in mind that there are value and quantity limits for duty relief, some (e.g. excise) goods have special rules, while other goods need import licenese or are subject to import prohibition. Pets need pet passport for travel. Cash of a value of EUR 10 000 or more (or its equivalent in other currencies) shall be declared to the customs authority.
Please consult these general rules before your travel at this website:
https://nav.gov.hu/nav/kiadvanyok/utastaj/utastajekoztato/utastajekoztato_2020