Glossary entry (derived from question below)
English term or phrase:
united kingdom
Persian (Farsi) translation:
پادشاهی متحد بریتانیای کبیر و ایرلند شمالی
English term
united kingdom
ترجمه ای که مناسب باشد و با
Great Britain
و
England
متفاوت باشد.
با تشکر
Proposed translations
Australia
NAATI & ISO 17100 certified, MNZSTI
Native in: Persian (Farsi) 
Works in: Persian (Farsi) to English, English to Persian (Farsi)
پادشاهی متحد بریتانیای کبیر و ایرلند شمالی
Iran
Corpus-based Translation
Native in: Persian (Farsi)
Works in: English to Persian (Farsi), Persian (Farsi) to English, Dari to English
)پادشاهی متحد (بریتانیای کبیر و ایرلند شمالی
United Kingdom
Well Timed, First Quality Translation
Native in: Persian (Farsi)
Works in: English to Persian (Farsi), French to Persian (Farsi), Persian (Farsi) to English, and 1 more.
بریتانیای کبیر
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Note added at 4 mins (2023-03-15 10:59:26 GMT)
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In history we have بریتانیای کبیر or بریتانیای بزرگ which covers all british territories around the world.
Experienced qualified Farsi translator
Native in: Persian (Farsi)
Works in: English to Persian (Farsi), French to Persian (Farsi), Persian (Farsi) to English, and 4 more.
ممالک متحده بریتانیا/پادشاهی انگلستان
Iran
Translation: A Bridge among minds
Native in: Persian (Farsi) 
, English
Works in: Persian (Farsi) to English, English to Persian (Farsi)
پادشاهی متحد بریتانیای کبیر
به اختصار بریتانیا
Spain
مترجم و محقق ترجمه
Native in: Baluchi , Persian (Farsi)
Works in: Persian (Farsi) to English, English to Persian (Farsi)
Discussion
https://en.wikipedia.org/wiki/Great_Britain
"United Kingdom" is short for "The United Kingdom of Great Britain and Northern Ireland". It comprises England, Scotland, Wales, and Northern Ireland.
https://en.wikipedia.org/wiki/United_Kingdom
The "British Empire" was composed of the dominions, colonies, protectorates, mandates, and other territories ruled or administered by the United Kingdom and its predecessor states
https://en.wikipedia.org/wiki/British_Empire
For further discussion see, e.g.,
https://www.bbc.com/news/magazine-37058920
So, the right choice of words in English depends on the intended use.