Is there any immigration check when flying from Southern Ireland to the UK?

No. According to the regulations of the British government, regardless of whether passengers are entering from England, Scotland, Wales or Southern Ireland, they do not need to fill in a passenger locator form before traveling, and they do not need to undergo nucleic acid testing or quarantine after entry. The United Kingdom is a sovereign country in northwest Europe, located near the northwest coast of the European continent. It consists of the island of Great Britain, the northeastern part of the island of Ireland, and a series of smaller islands.