So United Kingdom is split into England, Scotland, Wales and Northern Ireland. Was all of it simply England at some point in history?

The British Isles suffered invasion from many different foreign powers and groups over a very long history. I'll try to answer your questions simply, but someone else may be able to expand further if you have more questions.

Before the Roman conquest of Britania, the people living on the British Isles were a sort of hodgepodge of different cultures and groups, mostly sticking to their own areas. The islands themselves have been continuously inhabited since prehistoric times. Iron Age Britain was dominated by tribal influences, but most of these tribes are considered to have belonged to a broadly defined Celtic culture. The general geography of the island group is probably the main reason why distinct groups formed and remained relatively isolated.

In 43 AD Rome began its slow invasion/conquest of Britain. Emperor Claudius installed Aulus Plautius as the first governor of Roman Britain. Rome ruled lower England very effectively, but it struggled with the geographic features separating lower England and Wales and didn't control Wales until 48 AD. Rome built Hadrian's Wall beginning in 122 AD, separating lower England from Scotland (where historically the Picts resided and were common raiders of Roman border settlements).

Rome never controlled any territory north of the wall, so ancient Briton culture (including the Picts) remained the dominant social force. Rome tried many times to conquer the Picts and other ancient Briton tribes that represented a constant nuissance. However, around the late 4th century AD, for a plethora of complicated reasons I won't get into, Rome abandoned the island and left the Britons, who now consisted of many ethnic groups from all over Europe, on their own.

Your questions seem to center on how the four entities came to be united under the crown. On Christmas day 1066 William I was crowned King of England. Almost immediately after Normans began pushing into the Welsh Marches. It wasn't until 1282 that Edward I established full control over Wales. Edward's son, Edward II was created Prince of Wales and ever since the first in line to the throne has been granted this title. England has controlled Wales, more or less, since Edward I.

Scotland is a different story. The Kingdom of Scotland was formed in 843 AD. It mostly controlled the northern third of the island, and for a long time was England's adversary politically and socially. However, through typical medieval royal positioning in 1603 the King of Scotland, James IV was determined to be the heir to the throne of England when Elizabeth I died without issue. As such, both Kingdoms were united in personal union under the monarchy of James I. In 1707 Parliament passed the Acts of Union, officially joining the two kingdoms and they have remained so ever since.

England long sought to conquer Ireland, and they fought for a long time. In 1155 Pope Adrian IV issued a bull granting Henry II of England lordship over Ireland, and he invaded. A peace treaty resulted in Ireland being decided between Henry II and the Irish "High King". For all intents and purposes, though, England ruled Ireland during this time and was the dominant force. The black death caused many deaths among the Norman lords and English settlers in Ireland, but mostly spared the native Irish population, leading to a resurgence of Gaelic (Irish) power. England was driven to only controlling isolated areas of Ireland. By the end of the 1400s England had little authority in Ireland. In 1532 Henry VIII split from the Catholic church. Scotland, Wales and lower England supported and adopted Protestantism, but the Irish remained fiercely Catholic, which led to deep division within Irish society. This led to hundreds of years of fighting between the two as England feared that Ireland could be used as a base for Catholic forces trying to overthrow the Protestant government of England.

In 1536 Henry VIII tried to reconquer Ireland. In 1541 he made Ireland a Kingdom upgrading it from a lordship. He was proclaimed King of Ireland. Elizabeth I and James I would eventually solidify control over Ireland, but we're unsuccessful in converting the Irish away from Catholicism. The policy from the mid-1700s forward was that of colonisation. English nobles were granted vast estates and lands in Ireland, called plantations. These British protestants would form a ruling class in Irish society that would become the catalyst for future rebellion.

In the 1840s Ireland suffered the Great Famine, brought on by a potato blight. Over a million people emigrated from Ireland, mostly to the USA. This time also saw the rise of Irish Nationalism, especially among devout Catholics who opposed protestant rulers. In 1916 an armed rebellion took place. Irish MPs almost universally supported Home Rule. In 1918 the radical Irish Republican party gained enough seats to establish a firm control over Ireland and set up an Irish Parliament. They declared independence from England, and that began the Irish War of Independence. In 1921 the Anglo-Irish treaty was signed, portioning off Northen Ireland as a home rule state under the British crown, and creating the free state of Ireland, which was still a British dominion (like Canada today). However, in 1949 Ireland declared itself a Republic and ceased to be a part of the British Commonwealth, no longer having any constitutional or other ties to the UK. Northern Ireland, dominated by protestants, remained part of the commonwealth.