The EU Citizenship Programme by EU Passport allows you to travel, live and work visa-free and permit-free all over the European Union, including the United Kingdom. Since Hungary is a member of the EU, the Hungarian Citizenship/Passport can be termed as an EU citizenship. You have the option to live and work in all countries which are registered with the EU, including the United Kingdom.
Furthermore, Hungarian citizens can travel visa-free to many countries outside the EU, including Brazil, Japan, Argentina, Canada, South Africa and many more. Also, Hungary has respectable foreign relations with almost all countries. Therefore, the Hungarian passport will help you get a visa to any other country where visa-free travel does not apply.