This is an interesting what-if - improbable as all hell, but then so was Tunguska.
1. I have not been able to determine whereabouts of the Royal family on June 28-29 - Edward VII had just returned from a state visit to Reval, in Russia, on June 9-13, but I have not been able to determine where he was on the day in question.
However, it is worth noting that Parliament was
adjourned on June 24. Which means there is a strong likelihood that the bulk of the members of the House (and certainly the Lords) are out of town, and thus survive. That might be less true of the cabinet, of course, since they would be more likely at their offices in London.
2. It's curious that there is a general assumption that such a blast would destroy the British Empire at a blow. I think the Empire was more resilient than that at that time, and that it is quite possible - even probable - that the tragedy helps bring it closer together in the short term. Electric Monk may be on to something in his idea that this might even create a new impetus to a real federation with the Dominions. If the British and Dominion leaders were smart, they'd do just that.
It's true that in some of the non-white colonies, such a disaster would be seen as a divine judgment - or at least a wonderful opportunity - by leaders of some subject peoples, particularly in the Raj. Risings might happen, but I would expect the Raj to put them down pretty ruthlessly.
3. European politics: It's hard to think that World War I, if it happens,wouldn't unfold quite differently than it does in OTL, and not just because key people (Asquith, Grey, Churchill, etc.) would be dead. The Royal Navy and the military would survive essentially intact, but Britain would have a suddenly new set of urgent priorities - rebuilding London and Essex (and yes, I think they would be rebuilt). British finance - the financial leaders, the exchanges, the financial records, the monetary reserves - would be decimated, and that would likely bring on a severe world recession, if not depression, given London's status as financier to most of the world. Meanwhile, it's quite probable that growing popular resentment and hatred of Britain in Germany, especially in its leadership circles, would be transformed to profound sympathy. That might make an Anglo-German rapprochement more likely. Thoughts of exploiting British weakness would be offset by profound fear given the suddenness and magnitude of this hammer blow from the heavens, and that might remove a lot of the eagerness to go to war across Europe.
4. It's harder to know what this would mean for British politics. Asquith's Liberal government had been in power for a few years, and was still quite popular; Asquith and much of his cabinet would be dead, and the realm would certainly rally around the government in the short run; it could hardly be blamed for such an inconceivable event. Whether the new junior leadership would be up to the task is harder to say. More likely you would see a national government formed, composing Tory and even Labour leadership, and that would last until at least the next election, whenever it happened. That would reduce the likelihood of the looming constitutional crisis over the House of Lords' power over finance bills, but would reduce it to a nullity in any event since none of the Lords would likely muster much resistance against the emergency program of assistance and rebuilding that would put forward by the government.
5. There would quite obviously be a great deal of interest in astronomy and aerospace science. The heavens would be looked on with a new and powerful sense of fear. The optimism of the Edwardian world would be shaken, but also redirected to acquiring greater knowledge of such celestial bodies, and possible means to warding them off. Unfortunately, the means to really accomplish either were still generations off even with unlimited funding levels and public support. Could that zeal sustain itself for so long?