This was a real entity resulting from a phrase coined by a local Conservative MP when describing the Council, and taken to heart by the residents of Sheffield in the 1980s when said Labour Council actually took to flying a red flag over the town hall. There were even roadsigns leading to the city marked with 'You are now entering the Socialist Republic of South Yorkshire'. It was also called the People's Republic of South Yorkshire. It was at its height during the Miners' Strike of 1984-85, when bizarrely it could be said to have a type of monarch as its leader, Arthur Scargill, who was leader of the National Union of Mineworkers, was known by the press and locals alike as 'King Arthur'. The fact that he was pretty much a Communist lends even more irony to his nickname.
The end of the Republic occured when the local Liberal Democrats stormed the Council buildings in elections held during the early 90s. In something of an irony, the local Conservative MP who had coined the term, Irvine Patnick, was booted out and replaced by a LibDem one. Although Labour gleefully regained control of the Council in subsequent elections, the Republic has not been re-established.
It is Thande's intention to declare a Second People's Socialist Republic of South Yorkshire at some point and in keeping with tradition he says it'll retain a monarch in the shape of the Queen.