This a complicated question to answer as it is a highly contentious issue. The British were less responding to the Troubles and more actively creating an environment conducive for the situation to spiral out of control. There were two major early policies of the Troubles that determined its destructive course. First, the British government introduced the counter-productive policy of internment in 1971. Internment introduced a new style of prison and camps which bypassed normal legal procedures in the hopes that the internees would confess on their allies. Most of these internment policies disproportionately affected Catholic communities, even though they did not commit the majority of violence within Northern Ireland. Protestant loyalists paramilitaries committed the majority of violence along with covert acts by the Ulster Volunteer Force and covert acts by British special forces between 1971-75 (the first major bombing was committed by Protestants-UPV- in 1969). The 1972 disestablishment of the Stormont Parliament (the independent parliament of Northern Ireland created in the aftermath of the Civil War) and reassertion of direct control by the British state meant that the British government directly intervened within Northern Irish politics. In short, the UK forces (civilian and military) were no longer seen, justifiably, as neutral arbiters who could guarantee the peace.

For UK soldiers, most of them had adapted a mentality that the Catholics were the cause of the sectarian problems. They also looked upon the Protestant militias and paramilitaries as their natural allies within the region. This meant that the UK troops were often willfully blind to Protestant violence. The army and special forces also harassed Catholic neighborhoods and conducted arbitrary searches and seizures. The Protestant paramilitaries often did the same thing, but at night and more violently, so it was harder to tell the difference between UK troops' actions and those of the paramilitaries. The army did not help its case by conducting daylight patrols with many with many of these paramilitaries.

The most infamous special forces response was Bloody Sunday in January 1972. The NICRA (Northern Irish Civil Rights Association) group conducted a peaceful march against internment and the British paratroopers opened fire and killed 13 people. The troopers initially claimed that they were fired upon first, but the 2010 Saville Report concluded that the paratroopers lied about being fired upon.

World opinion at first bought into the idea that the IRA was a terrorist group and British actions were justified. However the escalation of violence precipitated by Bloody Sunday turns some opinion towards the IRA and against the British. Irish-American groups in particularly started to put pressure against the British. Also civil rights activists were also now more sensitive towards the Catholic side. Also the IRA were quite adept at propaganda and using the overreactions of British and protestants among world opinion. Yet there was still a sizable body of world opinion that saw the IRA still as a terrorist group and British actions as harsh but necessary (see for example, Tom Clancy's popular novel Patriot Games which paints a splinter faction of the IRA as Marxist-inspired cowards). But the big turning point was 1981 was Bobby Sands hunger strike and subsequent death which was much harder for the British to justify.

Sources

Bew, Paul, Peter Gibbon, Henry Patterson, and Paul Bew. Northern Ireland, 1921-1996: Political Forces and Social Classes. London: Serif, 1996.

CAIN Web Service - Conflict and Politics in Northern Ireland http://cain.ulst.ac.uk/index.html

Whyte, John Henry, and Garret FitzGerald. Interpreting Northern Ireland. Oxford: Clarendon Press, 1990.