The answer is "yes, probably," but I have been unable to locate specific numbers. If you're looking for a bodycount of the Queen's (or King's) Guard, nobody that I know of has compiled such a list. Obviously, the units from which the Guards are drawn often see combat overseas, and have fought in battle over the past centuries, but the likeliest incident that I immediately thought of (this is actually linked from the Wikipedia page on the Queen's Guard) was during the Gordon Riots. This was, to the best of my knowledge, the only time when members of the Guard were in a position to fire on people in the city of London, and then actually did so.

As background, the Gordon Riots marked a period of severe civil unrest in London, 1780, as a result of anti-Catholic sentiment and other contributing factors that are not worth getting into here (but mostly boil down into "Lord Charles Gordon was at fault and that's why we named it after him"). Long story short, on June 2 a number of demonstrators marched on Parliament to deliver a petition, and while the debates were going on inside the demonstrators outside were getting themselves riled up to the point where Members of Parliament were apparently at risk of being killed. The Guards were obliged to clear a path through the crowd in order to allow Parliament to exit, which they did by eleven o'clock in the evening. This is very probably the best bet to answer your question: the Palace of Westminster where Parliament meets is technically a royal residence.

That being said, it seems unlikely that anybody was actually killed during this initial incident. (Of course, the soldiers were armed with musket and bayonet, which aren't great for nonlethal crowd control because they're weapons meant for killing people outright -- see the Boston Massacre for one example of when things went tits-up like that.) Anyways, in the days following the unrest outside of Parliament, the rioters went rampaging through the streets smashing stuff, but most of their targets appear to have been non-royal residences. Among the buildings ransacked were several of the prisons, where the prisoners were set free and mostly escaped recapture; foreign embassies, especially of Catholic nations; the houses of wealthy Catholics; and a few houses of local government officials or nobles perceived to be pro-Catholic in their stance. People definitely got killed by soldiers during this later action; the numbers that I am seeing are 210 killed, 75 died in hospital, and 173 wounded. Among the units deployed were units of the Guards, who distinguished themselves defending the Bank of England.

We have no way of knowing exactly how many of the dead can be ascribed to the work of the Guards -- they were not the only regular soldiers present in London at the time, and the city drew upon the support of local county militias to supplement their forces (incidentally, these irregulars seem to have acquitted themselves better during the actual riots). Please also note that the purpose of the rioters was never to attack the king, or his properties: it was an outpouring of anti-Catholic hatred that manifested in attacks on more low-hanging targets. Most of the estates more typically thought of as royal residences (Buckingham Palace in England, Balmoral Castle in Scotland) have more or less escaped such violence over the years.

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For further reading:

McCormack, Matthew. “Supporting the Civil Power: Citizen Soldiers and the Gordon Riots.” The London Journal 37 (2012): 27–41.

Rudé, George F. E. “The Gordon Riots: A Study of the Rioters and their Victims.” Transactions of the Royal Historical Society 6 (1956): 93–114.

Does anyone know if, in today's world, the Queen's Guard are trained and authorized to use lethal force if necessary?

Tangential question: Did the guards at Versailles kill any peasants that were storming the castle during the French Revolution? Or did Versailles not have armed guards who were trained and ready to fight?

Hello everyone,

A quick reminder for both first time vistors, and those who are apt to forget the rules here. We've already had to remove several joke comments, several "I don't know, but here is one security incident I know of no one died during" comments, and one about how wonderful the mod team is how much the mods suck. The mission of /r/AskHistorians is to provide users with in-depth and comprehensive responses, and our rules are intended to facilitate that purpose, so those were removed, and further rulesbreakers will be considered forewarned.

An additional important reminder ought to be made with a question like this. If such an incident has occurred, hopefully someone will be along to write about the matter in due time. But if it has never happened, a response that is simply "Nope" or "Not that I'm aware of!" will not be sufficient, and thus with a response in the negative, we would expect to see a demonstration of familiarity with the history the Palace guards, so as to be reasonably confident that it is the answer rather than ungrounded speculation.

Of course, we know that it can be frustrating to come in here from your frontpage or /r/all and see only [removed], but we ask for your patience and understanding. Great content is produced on this subreddit every day though, and we hope that while you wait, you will check out places they are featured, including Twitter, the Sunday Digest, the Monthly "Best Of" feature, and now, Facebook. It is very rare that a decent answer doesn't result in due time, so please do come check back on this thread in a few hours. If you think you might forget, send a Private Message to the Remind-Me bot, and it will ensure you don't!

Finally, while we always appreciate feedback, it is unfair to the OP to further derail this thread with META conversation, so if anyone has further questions or concerns, I would ask that they be directed to modmail, or a META thread. Thank you!

Edit: As this seems to have scored big on /r/All, and a lot of people unfamiliar with the sub are tracking in here, here is a quick breakdown of the removed comments for the curious, although it is likely already out of date from when I started compiling it given the speed of responses flowing in:

• 11 comments are "I know of this incident where they didn't kill someone". As stated above, giving one or two examples of it not happening doesn't answer the question unless you can contextualize it to the larger history the Guard.
• 2 comments are just "Yes" and 1 comment is just "No". 2 at least made partial sentences. I appreciate the consistency.
• 1 is suggesting this should be posted to /r/AskReddit with a serious tag. If what you want is a thread which allows broader speculation then here, then I encourage you to follow /u/SuperHICAS' advice. If someone does, I'll even edit to link it here.
• 8 are about how much they love the mod team the mod team is a bunch of "massively absorbed c**ts".
• Update: And now a visible answer. Enjoy.