It doesn’t have to do with profit, but rather protection, protection for the Northern Protestants and as protection for England herself against having an enemy right next to her.
Britain has been in Ireland for nigh on 800 years so part of it is tradition. It started when King Dermott MacMurragh requested Norman and Welsh assistance to recover his throne back in in 1169. His effort ultimately failed when his son was slain as a beast would be slain for market, thus taking the heart out of Dermott. But the connection was forged.
Then, under Henry II, the English began settling in Ireland during the 12th century. This was because the system of male primogeniture in England left too many young men without land. Some were pushed into the Crusades, some to the Church, and some to Ireland. They pushed the locals off the land where necessary and claimed it for themselves. But it wasn’t until 1603 that a victory over the Irish in Ulster allowed Britain complete control of Ireland.
Ulster continued to be a troublesome province, so the English brought in Protestant Scots to farm the land (including a few of my ancestors) as long as they never sold it back to the Irish. Then after the English Civil War, Cromwell paid his troops with more Irish land, confiscated from the Irish who were shunted over to poor quality land in Connaught.
An important reason for the English desire to control Ireland was for Englishmen on Ireland to help defend Britain against raids. Early on it was raids by the Vikings, then problems with the Spanish. In 1798 it was the French that invaded, so that in 1801 England actually melded Ireland and England together as one country. Then, during World War II, the bulk of Ireland, the Republic of Ireland, maintained strict neutrality, leaving England uncertain as to whether she would be safe from invasion from that side.
Britain left Ireland in 1922 after 800 years of occupation, when a peace agreement was made to grant the present day Republic of Ireland autonomy as the Irish Free State, whilst Britain retained control of Northern Ireland.
The descendants of the Protestant Scots in the north wish to retain their connection to Britain and seek protection from the IRA. Thus, Britain cannot simply abandon those people to the not so gentle ways of the worst of the Catholics, and she wants a foothold on Ireland in case some enemy decides to attack from that direction.