In Spain there were similar attempts to suppress Catalan and Basque to the English's attempts on their minorities. Why were the English so successful, while the Spanish weren't?
The_Chieftain_WG has talked about Ireland, I'll talk about Scotland.
Essentially, the key thing with the Scottish is that a lot of them do speak their "native" language/dialect: Scots. Scots is a dialect/language* that's fairly similar to English. Think something like "Aye, the wee lass" for a very stereotypical example. Or the words of "Auld Lang Syne", which was written by the famous Scottish poet Burns.
Traditionally, lowlanders spoke Scots (a germanic language based on Anglo-Saxon, like English, but one which developed in a different way), while highlanders spoke a Gaelic (ie Celtic) language similar to Irish. Which one was the "real" Scottish language could be controversial. James VI used to refer to Gaelic as Irish (implying it was a foreign language).
Anyway. After 1600, with the spread of literacy and the personal union of England and Scotland, Scots began to evolve to be more similar to "standard" English (as did England's own regional dialects: while Britain still has much more diversity of accents and regional words per square mile than most countries, it's much less varied than in 1600), though still a bit different. Saying this, the government did generally dissuade people from using local words, with newspapers, books, schooling and officialdom using "standard" English; of course, this was also the case across most of England, with local dialects in places like Yorkshire or Devon being a mark of low class, while the educated upper class spoke RP, aka "the Queen's English".
Also, the population of the Highlands didn't grow anywhere near as rapidly as the industrialising lowlands (which had always had the advantage of better farming land anyway), and the Highland Clearances, combined with industrialisation, caused a lot of Highlanders to leave for places where they needed to use some form of Scots or even just English. Thus, the number of Gaelic speakers compared to Scots speakers fell considerably. In the 20th century, this was further affected by English (or Scots) media; there are BBC TV and radio programmes in Gaelic (my Mum often watches documentaries in Gaelic), but if you want to listen to pop music, or watch the latest blockbuster, a Scots speaker clearly has the advantage over a Gaelic speaker. While in the past Gaelic was discouraged by the government, today you can study it in school... but for a lot of kids, why would they want to? Thus, over the 20th century, Gaelic has fallen enough that all Scottish people speak Scots, and a few also speak Gaelic. But by the mid-90s, there were only a handful of old people who could only speak Gaelic left.
The result today is a spectrum of dialectical strength, with some Scots speaking what is essentially English with a Scottish accent, while others might pepper their speech with words unknown to most English people, and even use different grammatical forms. Here's a bunch of Scots words, just to show you: Aboot, bairn, bonnie, brae, cooncil, doun, dreich, faither, fitba, flit, glaikit, gowk, heid, hoose, ken, kirk, laddie, lang, lassie, mither, nane, poke, rare, scunner, speir, stooshie, stramash, threap, wean. Some, you might have heard before (I imagine you've heard "lassie" before), or be able to work out the meaning (Kirk is Church, for example).
If you'd like to hear some examples of people speaking Scots, have a look at this site: http://www.ayecan.com/listen_to_scots.html
*Whether it counts as a dialect or language can be a bit controversial, so I'm not going to get really into it. The difference is essentially semantics, but one with symbolic importance to some people. The point is it's similar to English, but still different enough that, say, an American or Australian would find it easier to understand English than Scots.
I'm not entirely sure I understand the basis of the question.
It is certainly true that the default language across Ireland is English, but there are parts of the country in the West and South known as The Gaeltacht where the daily spoken language is Irish. Further, there are households in the rest of the country where such is the case. A cousin of mine is a case in point: He lives in Dublin, but his children go to an Irish language school, and they speak Irish at home.
There are two official languages in the country. This has a number of effects. One is artificial. Irish is a mandatory course for school children, and at least a basic knowledge is a pre-requisite for university. (Not that it is ever used, but if you don't have English, Irish, Maths and a Third Language, you generally will not meet minimum entry requirements). This alone has ensured that Irish is not lost. Anyone in the Army must have basic Irish knowledge: All drill commands are in Irish. There are a couple of units where Irish is the spoken language. A particular problem has arisen in the judicial system. As an official language, the accused may have his case heard in Irish. The problem is finding a jury of enough Gaelgors who are fluent enough to keep up. The issues of translations and eligibility pool got to the Supreme Court. You can imagine the other problems of a similar nature.
I am not familiar with the Spanish equivalents, but over the several hundred years that the British were in charge in Ireland, not only did they suppress the language and culture, but it also simply made sense for Irish folks to learn English. Dublin was the second city of the empire. England was the closest trading partner. In order to better operate, folks had to learn English for their own benefit. There may be a correlation.