The British Empire did not exist in the Middle Ages. In the early Middle Ages, England was part of other empires:
In 1066, William of Normandy conquered England. Other lands conquered by the Normans included parts of the south of Italy and during the Crusades the Holy Land.
During the reign of Henry II, England was part of the Angevin Empire, which included Ireland and most of western France.
The Norman and Angevin Empires were not overseas empires and their rulers regarded them as single realms. They were not 'colonies'.
However, medieval kings sought to acquire ever-wider lands by warfare or marriage and conquered lands, like Wales and Ireland, were run by English administrators.
Battle of Poitiers, France, 1356 - one of the battles of the Hundred Years' War
During the Middle Ages, the kings of England tried to conquer other countries:
In 1169, Normans from south Wales invaded Ireland. In 1171, Henry II went to Ireland to make sure that their conquests were made part of his Angevin Empire. In the years that followed, about half of the island was over-run by Normans, English and Welsh.
In 1277, Edward I invaded and conquered north Wales.
During the Hundred Years' War (1337‒1453), Edward III and Henry V conquered large areas of France, but by 1453 the only land still in English hands was Calais (now in France), which was later lost in 1558.
By 1500 the kings of England had lost control of all of Ireland except for coastal towns and an area around Dublin known as the 'Pale'.