The islands are very near England, I can't understand how they become mere dependencies.
The reasons why they didn't become fully integrated with England were different between the Isle of Man and the channel Islands.
The Isle of Man had never been part of England before the Norman conquest, and it was not part of England after the Norman conquest. It had been ruled by Norsemen or Vikings since about 850 AD. From about 1079, Man was part of the Kingdom of Man and the Isles. This Kingdom was split in two in 1164. Both these Kingdoms were nominally subject to the Kings of Norway.
In 1266, there was fighting between the Norwegians and the Scots and the Norwegians ceded the islands to Scotland in return for some money. The Manx did not really recognize this shift in overlords until 1275 when they were defeated by the Scots in the Battle of Ronaldsway.
In 1290, King Edward I of England seized Man, and it remained English until Robert the Bruce of Scotland took it back in 1313.
Man was kicked back and forth between England and Scotland.
In 1405, King Henry IV granted the island to the Stanley family as a feudal fief (the feudal fee was to render homage and give two falcons to the Kings of England when they were crowned - which was not a very burdensome relationship.)
The Stanley family governed the island until the English civil war, when they were briefly ousted by the Parliamentary side, but the Stanleys recovered control with the restoration.
By the 1700s, Man had become a smuggling base. In 1765, the British Parliament, to suppress the smuggling purchased the Stanley family rights (but not the 'National rights') pertaining to the Isle of Man. This allowed Parliament to control foreign policy, customs duties and trade laws.
The laws and customs internal to Man remained largely unchanged.
In short, the Isle of Man, though owing fealty to the Monarchs of England since 1405 (and in various earlier periods), was never part of England (or Scotland, though it owed fealty to the Scottish Monarchs at various times).
When the British Parliament gained some control over the external and trade affairs of the Island, they never incorporated it into Britain, and its internal laws and governance structures remain distinct.
The Channel Islands are two separate 'bailiwicks' or administrations (The Bailiwick of Guernsey and the Bailiwick of Jersey), each with separate laws and legislatures. The Islands were annexed to the Duchy of Normandy in 933 AD.
In 1259, King Henry III surrendered his claim and title to the Duchy of Normandy, but retained the Channel Islands, which, since then have been possessions of the Crown, but not part of England. (The Queen is often referred to as the Duke of Normandy in her role as sovereign of the Channel Islands, but this has not been formally true since the Treaty of Paris of 1259.)
The Channel islands have been invaded, and briefly occupied by the French and the Germans on several occasions, but have always reverted to the English Crown.
The Channel Islands have been possessions of the Crown of England since 1066, but have never been part of England.