At no point in the past 200 years (and more) has migration from Ireland (the whole island) to Great Britain (the whole island) been controlled, and vice versa. Not that many British people want to go to Ireland; the movement has always been the other way. But movement has been free and most (all?) of the time, no one has had to show a passport, obtain a visa or report to the police when they move from Ireland to Britain.
In 1841, Ireland had a population of about 8 million. That dropped to 6.5 million by 1851 thanks to deaths by starvation in the Great Famine and the emigration of around a million people, most to the USA or Britain.
The mis-named Irish Free State was an unpleasant clerical-fascist dictatorship for the first forty or so years of its existence (never forget that in May 1945 Taoiseach Eamonn de Valera went to the German Embassy in neutral Dublin to express his Condolences on the death of Hitler) and millions left to escape poverty, the priests and the nuns. By 1951 the population of Ireland had dropped to 4.3 million. Most emigrants headed for Great Britain and, in many cases, war-work or the construction industry.
Northern Ireland, brought into being after World War One by reactionary Protestants and continuously a nasty area of religious persecution and sectarian violence, also sent its contingents of migrants to Great Britain - but even at the height of IRA violence in England there were no restrictions on movement. Northern Ireland, after all, was part of the Union and in the Union there was, of course, free movement of goods and people.
In 2001 Ireland had a population of 5.6 million. In Great Britain at that date, about 6 million people out of a population of around 60 million had at least one Irish grandparent.
The door has always been open.
"The Right Honourable Member for Woodford [Winston Churchill] thinks that the 'wogs' begin at Calais" - Labour MP George Wigg in the House of Commons, 1949
Mr Cameron thinks so too; so does much of the British population.
They should be reminded of our open back door and asked why they are so keen to close the front door - indeed, keen to brick it up, blow it up, anything in fact ...
[ All the information on Irish migration from Wikipedia's "Irish migration to Great Britain"]