How did invasions shape English/British identity?
Please note that "English" identity is slightly different from "British" identity. Great Britain incorporates England, Scotland, Wales, and Northern Ireland. Also, due to Britain's colonial rule in the 19th and 20th centuries, there are other countries, too, that claim aspects of "British" identity and culture, countries as distinct as Australia, India, and the Bahamas.
The first group to invade and conquer Britain was the Romans. They arrived in approximately 43 AD and remained until 420 AD. At that time, what is now Great Britain was then referred to as Britannia. The Romans introduced their bridge technology and also constructed bath houses. The town of Bath in England is appropriately named for its Roman-style baths. From 307 to 337 AD, Constantine the Great ruled the Roman Empire and introduced Christianity as the official religion of the empire, which included Britannia.
About a quarter into the fifth-century, the original Britannic people, said to have been of Celtic origin, plotted to get the Romans out of the country. They invited in Germanic tribes -- the Angles, Jutes, Frisians, and Saxons -- to expel the Romans. The guests, who came from what are now Germany and Denmark, were successful. However, they regarded the original Britannic people as weak. As a result, the Germanic tribes decided to take Britannia for themselves instead of returning it to the original people. Around 450 AD, Britannia became a land ruled by Germanic tribes.
It is from them that we get the term "Anglo-Saxon," which is the ethnic designation for all British people. The "Angles," one of the invading tribes, received their name from the native Brittanic people who, struck by their fair skin and hair, supposedly compared them to angels. A misprint in a manuscript or changes in pronunciation may have led to "angel" being converted to "Angle."
The Germanic tribes imposed their language instead of learning whatever tongue was spoken in Britannia. Old English, which was spoken from the fifth-century until ca. 1050, was a very Germanic language, using sounds and vocabulary from Old High German and Old Norse. The introduction of this language, which is the foundation of the English we speak today, is probably the most important effect of the Germanic conquest.
In 1066, however, England was invaded by William the Conqueror of Normandy. From ca. 1100-1500, the English language took on more of a French influence. The French took over the royal court. Therefore, they influenced aspects of the language that interested them or directly concerned them. For instance, all language related to courtly life and chivalry is derived from French. Much of the vocabulary we currently use that is related to nature, gardening, cuisine, law and government, music and entertainment, etc., is derived from French.
In reference to the court, many customs, too, were of French origin. The Germanic peoples who had previously occupied royal positions were not very interested in the ceremonial functions that now characterize royalty. It was the French who introduced these customs. They also introduced the romance (roman), or courtly poetic tales, as a form of entertainment. During this period, characterized in literature and linguistics as the Middle English period, we get tales such as Sir Gawain and the Green Knight and, later, The Canterbury Tales. The latter was concerned less with the court and more with middle-class life.
I would argue that these early invasions -- Roman, Germanic, and Norman -- most strongly impacted English identity and language.