The myth that England has not been successfully invaded since 1066 requires a certain amount of special pleading - most notably in the case of a Dutch prince expelling the legitimate king in 1688, but also in terms of the significant numbers of non-English forces involved with Henry VII, Edward IV and Henry II as they came to power.
A less well-known edge case is the French invasion of 1216. This was part of the ongoing conflict between King John and his barons; after he attempted to weasel out of Magna Carta, signed the previous year. The Barons appealed to Prince Louis of France, later King Louis VIII the Lion, to take power, and on 21 May 1216, 800 years ago today, he landed in Thanet. King John fled from London to Winchester, and Louis advanced to the capital where he was (the chronicles say) welcomed by the citizens and proclaimed king. Winchester fell soon after and John fled north; barons joined Louis rapidly (including the King's half-brother, William Longespée, the Earl of Salisbury), giving him control over most of southern England.
It's quite likely that Louis would have won if John had lived to pursue and lose the war (and he did tend to lose wars). But in October he unexpectedly died in Newark of dysentery at the age of 49, and was buried in Worcester cathedral, nowhere else being conveniently under Plantagenet control. (This was shortly after the royal treasure went astray crossing the tidal pools of the Wash.) John's heir was the nine-year-old Henry III, and the popular William Marshall, Earl of Pembroke, became regent. Marshall rapidly moved to offer the Barons concessions that John would not or could not have offered, including re-issuing Magna Carta ("but the boy-king really means it this time, unlike his dad"); he was a known factor, and the barons started switching back again. Louis was running out of money, and his invasion was formally condemned by the Pope; he proceeded to lose a couple of decisive battles on land and at sea, and eventually under the 1217 Treaty of Lambeth was paid to go away.
This was only 150 years after the Norman Conquest. France and England could easily have ended up united under a single king, with England a dependency; French would have been consolidated, rather than deprecated, as the official language of the state; Anglo-Norman elites would have concentrated much more on their family and property links with France (which were disrupted in our timeline by the consequences of John's losing his continental territories); probably there would have been less attention paid to Scotland and Ireland as a result. Often time travel stories are written about killing off a historical celebrity in his or her prime; a really mischievous time-traveller would provide antibiotics to King John in 1216 and save his life, thus ending the Plantagenet dynasty and causing major disruptions to world history.