Do you mean the United Kingdom of Great Britain? The one formed in 1707? Or just the island itself?

The big three for me would be the Spanish armada, the Grande Armée and operation sea lion.

So in that order:

The first was divine intervention, although a lot was done by English, sailors most of the ships were sunk or scuttled due to the harsh weather and limited knowledge of the coast line by the Spanish.

The second was the brilliance of Nelson in destroying the French and Spanish fleets in the battle of Trafalgar. This meant that Napoleon could never get his army over the channel no matter how big it got.

Finally the battle of Britain. A mixture of brave men and women, genius inventions and a country's will and determination. We never lost air superiority long enough that an invasion would be practical.

Basically it boils down to being an island nation that for 300 years ruled the waves. Any attack on the British mainland had to go by water and that's what put would be invaders off.

The has not been a successful invasion since the formation of The United Kingdom. In the middle ages saw quite a few changes of management, but it is quite difficult to define a 'foreign invasion'. The were occurrences where a claimant to the throne would have support from abroad.

Queen Isabella, the daughter and husband of the kings of France and England respectively, successfully invaded from France with the support of Roger Mortimer. They ruled together for a few years until they were disposed.

http://en.wikipedia.org/wiki/Invasion_of_England_(1326)

Earlier than this, Empress Matilda launched a successful invasion in similar circumstances. Both these invasions were carried out with supporters in England though, making it much easier to land and supply an army.