There will be no change to the rights and status of EU nationals living in the UK, nor UK nationals living in the EU, while the UK remains in the EU.
There are occasional political demonstrations in Budapest and elsewhere in the country. Some take place on or close to important national holidays with a political relevance, such as 15 March (anniversary of 1848 Revolution) and 23 October (anniversary of 1956 anti-Soviet Uprising). Peaceful political demonstrations have occasionally ended in violence. You should avoid all political demonstrations, monitor the media coverage of local events and be aware of your surroundings at all times.
Although there’s no recent history of terrorism in Hungary, attacks can’t be ruled out. See Terrorism
Around 700,000 British nationals visit Hungary each year.
Take out comprehensive travel and medical insurance before you travel.
If you’re abroad and you need emergency help from the UK government, contact the nearest British embassy, consulate or high commission.
The Overseas Business Risk service offers information and advice for British companies operating overseas on how to manage political, economic, and business security-related risks.