The thing is, they didn't. What you are refering to is the 'Act of Union' passed by Henry VIII in 1536 - a law that essentially merged the judiciary systems of England and Wales so that Wales effectively became a province of England. However, before this, various areas of Wales had been subjected to Anglo-Norman rule for centuries, in some places nearly 500 years.

At this point, I should note that Wales as a single political entity never really existed for a prolonged period of time before the Act of Union. There had been several unifications of the land that would become Wales, such as under Rhodri Mawr and Hywel Dda, but the land was normally divided among several small kingdoms, with Gwynedd, Powys, and Deheubarth being the most dominant (see this map).

The Welsh kingdoms of the Early Medieval Period (not including British kingdoms, such as Elmet) did indeed clash with the various Anglo-Saxon kingdoms, and it is certainly likely that there was near continuous border raids by opportunistic warriors of both sides. The Anglo-Saxon Chronicle records how, in the year 577, the cities of Gloucester, Cirencester, and Bath were taken from the Britons, suggesting Anglo-Saxon expansion up to the lower Severn Valley occurred in the late-6th century. Charles-Edwards is suspicious about the dating, given how the Chronicle is not a contemporary document, and how, according to Bede (EH 3.7), the core of the kingdom of the Gewisse was in the Thames valley as late as the 630s (Charles-Edwards, 2013: 381). That said, Bede records the first attested instance of a Northumbrian king in the borderlands of Wales (EH 2.2), an event also recorded in the Anglo-Saxon Chronicle (year 607), implying that the Anglo-Saxons were abutting the modern region of Wales at this time. The Mercians may have been involved at the time, given that much of the borderland between modern England and Wales was composed of Mercian tributary states (Charles-Edwards, 2013: 387-8), and their involvement alongside the Welsh can be interpreted as an early form of Mercian hegemony that encompassed part of Wales.

It is tempring to read into the testimony of these sources the same political situation of the eighth century, where each of the major Anglo-Saxon kingdoms had there own Briton 'hinterland', "a frontier across which Britons could be raided or forced to pay tribute, and new territory conquered" (Charles-Edwards, 2013: 281-3). However, Aethelfrith, the King of Northumbria at the battle of Chester, was said to have "ravaged the Britons more than all the great men of the English" (EH 1.34), and his successor Edwin supposedly conquered north Wales, including Anglesey (EH 2.5, 9), suggesting the early Anglo-Saxon kingdoms were focused on imperial expansion, likely establishing tributary states, including in North Wales. This was certainly not the end of Anglo-Saxon aggression against Wales, with the Anglo-Saxon Chronicle recording an expedition by Egbert against the people of North Wales (year 828), and it records how seven years later there was an alliance against Egbert composed of Welsh and Danes (year 835). Burhred was said to have also invaded North Wales (year 853). Welshmen are even said to fight alongside the Anglo-Saxons against the Northmen, with the Chronicle claiming they were subjects of Wessex (year 894).

So, there was interest in conquering the region of Wales during the Anglo-Saxon period, but it never amounted to a total loss of independence for the people. This would change, however, with the coming of the Normans.

After 1066 the Normans quickly entered South Wales, taking Gwent and attacking Deheubarth, as well as making gains in the North after the imprisonment of Gruffudd ap Cynan, king of Gwynedd. However, these gains were largely lost, and the Marcher Lords were established. These Marcher Lords were essentially independent save for their obligations to the king, free to wage war against the Welsh and to rule their lands as they saw fit. These new warlords could not utilise their full powers due to the ongoing Anglo-Norman civil war, the Anarchy, and in this time much of South Wales was retaken, with peace being made between Rhys ap Gruffudd of Deheubarth and Henry II, making Rhys the Justicar of South Wales, meaning he ruled in the name of the English king and had control over not just the Welsh, but also had some control over the Anglo-Normans in South Wales (Carr, 1995: 49). This kind of interaction between Welsh princes and the kings of England would become more normal, and Llewelyn Fawr even married the illegitimate daughter of King John of England, Joan, upon signing a peace with England. Indeed, it is telling that the Magna Carta actually included provisions for the return of Welsh land and hostages taken by the English (ch. 56 and 57).

Parts of North Wales were conquered by Henry III, Perfeddwlad, the region between the rivers Conwy and Dee, in the mid-13th century, but this was taken back by Gwynedd, but the end of a truly 'independent' Wales was to begin. Edward I invaded Wales in 1277, and the disunity of the Welsh is evident in how fast many Welsh lords surrendered to Edward, as Llewelyn ap Gruffudd took hostages to ensure their loyalty rather than maintaining a close relationship (Prestwich, 2007: 150-1). The result of this invasion was the return of Perfeddwlad to English control and the reduction of the territory of Gwynedd. This division was what caused the last major Welsh war in 1282, when Dafydd, Llewelyn's brother, rebelled against Edward I, gathering a great amount of Welsh support from throughout the country, which was quickly won by the English.

This last defeat finally saw the annexation of Wales by England, with some lands being given to Anglo-Norman lords, some lands being given to loyal Welshmen, and the rest being claimed by the crown. A series of castles were constructed around Wales by Edward I and garrisoned by loyal troops, effectively encircling Wales in a ring of iron and stone, a permanent reminder of English dominance. From this point on, there were only very minor threats to English dominance of Wales, including some internal rebellions and the intrigues of Owain Lawgoch, the last of the House of Aberffraw, the Kings of Gwynedd, who nearly invaded Wales with a French army, save one - Owain Glyndwr. Owain Glyndwr would wage a very impressive war against England, enticing several very powerful English lords to aid him, and even planned on dividing England in three, but he too was defeated. Despite these last few rebellions, between 1284 and 1400 the Welsh were fairly loyal subjects of the English, with many Welsh lords being quite prominent during the Hundred Years' War, and Welsh soldiers composing a great deal of English armies at this time (see Carr, 1968).

I hope I have shown how England has exerted some form of control over some if not most of Wales for a long time. Often this control came with military conquest, other times through political alliances and agreements, culminating in the complete annexation of Wales by Edward I. The Act of Union of 1536, which formally saw the inclusion of Wales within the English judiciary system, effectively ending Welsh independence, was only the last act in a long line of English ambitions.

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Bibliography:

A.D. Carr, 'Welshmen and the Hundred Years' War', Welsh Historical Review, vol. 4 (1968), 21-46 (here).

A.D. Carr, Medieval Wales (London, 1995).

T.M. Charles-Edwards, Wales and the Britons 350-1063 (Oxford, 2013).

M. Prestwich, Plantagenet England (Oxford, 2007).

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See also:

D. Carpenter, The Struggle for Mastery: Britain, 1066-1284 (Oxford, 2003).

While the ‘Acts of Union’ were passed in 1536, Wales itself had already lost its independence to England long before that. The final conquest of Wales by Edward I was in 1283.

I haven’t watched ‘The Last Kingdom’, but if it portrays Wales and England as being isolated from each other and without conflict then it would be remarkably incorrect. While the Anglo-Saxon kingdoms would fight battles with most (if not all) of the Brythonic kingdoms in Britain, the first conflict with one of the kingdoms in modern-day Wales would be in AD 616, when a Northumbrian force defeated a coalition of Welsh kings led by Selyf Sarffgadau of Powys in the battle of Chester. Wales would be annexed 667 years after the date of this battle, and that would be the result of many, many more conflicts.

As to why this took so long, an exhaustive answer would likely have to cover the entire history of conflict between Wales and England, but I can answer in a more succinct sense.

Firstly, the Welsh leaders would frequently exploit weaknesses found in England. To give two examples: by 1157 the kings of Gwynedd, Powys, and Deheubarth (the three independent Welsh kingdoms at the time) had all expanded their territory at the expense of England while it was in a civil war.
Llywelyn Fawr also participated in the first baron’s war and recaptured large amounts of territory in Wales.

Secondly, the kings of Wales, despite the size of their territory, were also capable of defeating the armies of England. Gruffydd ap Llywelyn would conquer Hereford by 1055, Cadwgan ap Bleddyn defeated the Normans in 1094, the kings of Deheubarth and Gwynedd defeated the Normans in 1136 at the battle of Crug Mawr, and Owain Gwynedd defeated Henry II’s army twice, in 1537 and in 1163 just to name a few examples.

Thirdly, the rough and difficult terrain also certainly posed an obstacle, Henry II’s invasion in 1163 was partially rebuffed due to his failed attempt at crossing the Berwyn mountains, and the mountains of Snowdonia stopped many invasions from reaching further into Gwynedd.

And finally, there wasn’t always a strict need to conquer Wales, many kings such as Alfred the Great, Harold Godwinson, and William the Conqueror achieved an overlordship of Wales, with most (or sometimes all) of the kings in Wales swearing fealty to them.

So to summarise, Wales and England were not isolated from each other, and many battles were fought between the two. Difficult terrain, combined with military competence, posed a significant obstacle, and moments of weakness within the English state would frequently be exploited by the Welsh kings. Additionally, although Wales was fully conquered by 1283, many English leaders had achieved a form of overlordship over the territory, so it was not always necessary to campaign against the kings of Wales.

Sources:
Davies, J. (2007). A History of Wales. London: Penguin Books, pp.97-157

Maund, K. (2006). The Welsh Kings: Warriors, Warlords and Princes. The History Press, pp.54-57

Bartrum, P.C. (1993). A Welsh Classical Dictionary. The National Library of Wales, p.669.