The original charter of the Magna Carta included a clause that stated that if 25 barons were to meet and agree that the King was defying the charter, they could overrule his authority. King John eventually rejected this, leading to a conflict known as the First Baron's War.

During this conflict, Prince Louis of France, who would later become King Louis VIII of France, was invited into England by rebel barons and proclaimed as King. Louis was able to capture London and several other towns and cities in Southern England. However, King John died shortly into the conflict and many barons switched over their support to the nine-year old King Henry III, whose regent was the famous knight William Marshal. After a series of victories at land and on the sea, Louis agreed to negotiate with Marshal, which ended up with him giving up his claims to England and returning to France.

Whether one wants to consider this an "invasion" can be a bit contentious. Louis was a foreign prince, and he came to England with foreign knights and foreign soldiers. However, he was invited into England by an English faction and it was the support of the English barons who allowed him to achieve his brief successes. Louis was not claiming England for France, after all, though had he remained King of England, the Kingdom would have potentially been united with France under a dynastic union after the death of his father.

No. England's closest and strongest enemy remained France, but the conflicts were mostly fought on the Continent. In later years the mighty English fleet kept the other would-be invaders out, the Dutch and the Spanish never managed to set foot on land. During the WWII the Germans were defeated by air, although lots of towns were bombed many miles inland so that would be the most destructive invasion.