I had not realized this, but the English Navy took significant damage from Exocet missiles fired on their boats in the Falklands War.
…the experience of the British fleet in the Falklands conflict illustrates the vulnerability of warships to low-flying missiles. In addition to the sinking of the HMS Sheffield and Sir Galahad, virtually every British ship was hit by at least one of Argentinian’s French-made Exocet missiles – a weapons system which was already 20 years old at the time.
Reportedly the only thing that saved the UK force from obliteration was that the Argentinians had got their missile altimeter settings wrong.
Exocet missile sinks HMS Sheffield during Falklands War (first 2 minutes):