One the whole, the answer is more or less the same. The major reason is one of demographics and resources, in that England, and southern England in particular (the modern Home Counties and Midlands) are much more fertile and capable of supporting arable agriculture much more intensively. You'll also notice that the areas of English control and settlement (in the Middle ages at least) in Ireland and Wales were those areas which were richest and best suited to this intensive arable agriculture (the south coast in Wales, and Leinster (South-East), particularly the Boyne and Suir/Barrow/Nore basins, in Ireland. The more marginal and pastoral upland areas were inherently much more difficult to conquer, settle and hold and this wasn't completed until well into the 17th century in Ireland.

This isn't to say that the process was entirely geographically deterministic. There were important socio-economic and political factors too, which go are also useful to understand why Scotland was never conquered (it was joined to England by a combination of marriage alliance and dynastic accident in 1603). In the middle of the first millennium AD, southern Britain (the future England) was socially and economically very similar to Ireland and Wales, consisting of small-scale kingdoms with (relatively) equal and non-hierarchical social structures and a (relatively) poor aristocracy tied to kings through personal links. (Many scholars refer to these as 'tribal' kingdoms, most recently Wickham, but also more influentially FJ Byrne for Ireland, although I personally think the term has too much modern baggage.) By the year 1000, things had changed and England was a relatively united single kingdom, with a much more stratified society and a very wealthy aristocracy and monarchy. Irish and Welsh kingdoms were bigger too, but they still operated in a much more traditional society, with multiple competing kingdoms and much poorer aristocracies. The reasons for these changes happening in England and not the 'Celtic' nations are many and not at all certain, but close contact with the rich Frankish kingdoms on the continent and the eradication of all-but-one of the Anglo-Saxon kingdoms by the Vikings in the 9th century are important factors. There's also the fact that the English economy developed in a way which allowed the extraction of much more surplus from the peasant majority, allowing for wealthier and more powerful political elites. So not only was England geographically better suited to produce more and support a higher population, but its society and economy also happened to evolve in a way in which these resources were concentrated into the hands of fewer, wealthier, more politically powerful aristocrats.

Still, the English dominance of its neighbours was by no means inevitable. If the Great Heathen Army had been less successful in wiping out the House of Wessex's rivals, there could well have been several competing English kingdoms throughout the Middle Ages. Similarly, Ireland appears to have been trending to a more 'normal' medieval politics in the twelfth century, with more powerful aristocracies and a politically active institutional church. Had it not been for Diarmait Mac Murchada's untimely death in 1171, Ireland (or Leinster at least) could have evolved very much along Scottish lines, an independent kingdom with strong links and influences from Anglo-Norman England.

In terms of sources, the relevant chapters of Chris Wickham's The Inheritance of Rome and Framing the Early Middle Ages go into detail on the socio-economic structures of Britain and Ireland in the early Middle Ages. FJ Byrne's Irish Kings and High Kings is the classic description of early Irish 'tribal' society: even though it hasn't really been replaced, it's still quite dated though. For the period when the English really start to take advantage of their resources and begin to dominate their neighbours, RR Davies' The First English Empire and David Carpenter's The Struggle for Mastery are good choices to get things started; Carpenter in particular balances a nice introductory narrative without losing the analytical aspects.