This almost certainly didn't happen during the 1982 Falklands War. During said war, the Royal Navy mainly used the main guns of its ships in support of ground troops, and to bombard airfields on the Falklands. I've seen no complaints about their accuracy there.

However, the Falklands War was not the only time the Royal Navy fought near the Falklands in the 20th Century. In December 1914, a Royal Navy squadron formed around the battlecruisers Invincible and Inflexible defeated the German Navy's East Asia Squadron in a battle now named for the islands. The German squadron, attempting to return home, had crossed the Pacific, and defeated a dysfunctional RN squadron off the coast of Chile at the battle of Coronel. They then attempted to raid the Falkland Islands, in order to destroy the British coaling station there. In response to the loss at Coronel, the RN despatched a strong squadron to the Falklands. Arriving the day before the German squadron, they were initially surprised when the German ships arrived on the 8th. However, they responded promptly, and the battlecruisers used their superior speed, firepower and gun range to destroy the German squadron. In doing so, they racked up abysmal hit ratios, scoring just a few hits, despite firing nearly all their ammunition. Poor understanding of the Coriolis force has been blamed for this - for example, Neil DeGrasse Tyson claims it was the reason here. Unfortunately, there are several other factors that are more likely to have caused this poor accuracy. The spotting tops on the battlecruisers, from which the fire was controlled, were positioned immediately in front of the funnels. This, combined with the direction of the wind, meant that the spotters were frequently blinded by the smoke from their own ship, as well as gun smoke. The Germans were zig-zagging to avoid the British fire. This surprised the British spotters, as the RN assumed that the Germans would, as the British did, follow a straight course to make their own gunnery better. The Falklands battle was fought at very long range for the time (12.5-16,000 yards), and British rangefinders were not very capable at such ranges. Instead, ranging in on targets had to be done through spotting the fall of shot, a rather wasteful and inaccurate practice, especially against a zig-zagging target. Additionally, the fire-control system in use lacked the ability to account for the roll of the ship, which can result in massive differences in the elevation of the ship's guns. The effects of the Coriolis force over ranges comparable to those used in the battle are small, and would likely have been swamped by any one of the other effects.

A reply to /u/vanavv

We can compute this.

The Coriolis coefficient is f = 2 \Omega sin(\phi), where \Omega is the rotation rate of the earth, \phi is the latitude. For the Falklands we have about 52' S. So f = 1.14e-4.

The earth's rotation rate at the equator is about 465.1 m/s, let's discount this to 440 m/s at the southerly latitude.

The Rossby number, giving the significance of the Coriolis effect, is given by Ro = U/(fL), where U is the product of the velocity vector of the system under consideration to the Coriolis effect. I don't know the shell velocity over its trajectory, so if /u/thefourthmaninaboat can give me that information we can do further computations. L is the length vector, so let's quote /u/thefourthmaninaboat and give it the max range which is generously about 15 km.