Sorry for your loss, England and the rest of the British family.
Is Charles already king? Or does he need some approval first?
Uh… you are aware that the Queen Mother is not the same as The Queen? England is not having a monarchy crisis just yet.
Me thinks someone is a bit disoriented here…
The Queen Mother had a very long life. If Queen Elizabeth II follows her path, Charles may probably not be a King for another 30 years.
Yes, and by then he might be dead. 
I wonder, is there any precedent for that sort of thing? That is, has it ever been the case that the heir apparent, who has himself produced an heir, dies before the reigning monarch’s rule is over? So when the reigning monarch finally does die, the succession skips a generation and the grandson/granddaughter takes the throne?
I’ve heard some talk that QE2 might abdicate the throne so that Charles can become king before he’s 84.
I think so. I think George III succeeded his grandfather, and the son of Edward III, Edward the Prince of Wales (aka the Black Prince) died before his father.
In order to answer the question: IF it had been Queen Elizabeth who had died, then Charles would become king at that instant. There is no need for “approval” by any other body, such as Parliament. The coronation might not occur for many months (such huge state functions take time to prepare), but he would be king immediately upon her death.
The expression, “The king is dead, long live the king” is the expression of that instant transmutation of power from the deceased king to the next king (or queen.)
Edward III (reigned 1327 - 1377) was succeeded by his grandson, Richard II. His son, Edward the Black Prince, died a year before his father, and Richard II took the throne.
Thank you, C K Dexter Haven, for the answer.
My astounding ignorance of all things English, or British, or Royal has been pointed out to me before.
Let us never speak of this again…
Actually, I believe it takes a few months because you’re not supposed to celebrate after the monarch dies. You should mourn for a while and then you can have all the pomp and circumstance of a coronation.
A grandson or granddaughter ascending the throne of a kingdom because the parent died is a not infrequent occurrence throughout the world’s history.
If you look, you could probably find many instances of this happening in every monarchical line.
I hereby sentence you to eat sausage, bubble, and squeak until you burst! 
Toad in the hole! Toad in the hole! Make him eat Toad in the hole!
So in my continuing adult education, tell me if I have this right…
The Queen Mum WAS the Queen until the kingship descended to her son, at which point HIS wife became queen? So the elder Queen is more or less forcibly retired?
No…I don’t think that’s quite right. Please, make corrections where necessary, folks…
The Queen Mum was Queen Elizabeth’s mother. Her husband was King (don’t know his name), but she was never queen, like Queen Elizabeth II’s husband is not the King of England.
The monarchy descends in a direct line - only a son or daughter of the monarch may become the next king or queen. Their spouse cannot. If the monarch dies with no heirs, then the crown moves to the next in line.
Or spotted dick, perhaps? 
The Queen Mum was Elizabeth’s mother. She was Queen as long as her husband was alive, but her authority derived from him. When he died, Elizabeth, the oldest child, became the reigning monarch, and her husband, Phillip became Prince Phillip, not King. He has no authority on his own. When Elizabeth dies, Charles becomes king.
The title Queen Mother is more of a courtesy title, like continuing to call former Presidents by that title after they leave office.
George VI.
I think it’s been adequately covered, but more properly, you have to distinguish between a REIGNING queen, and one that is simply titled “Queen” because she’s the spouse of the reigning king. Spouses of reigning queens are titled “Prince”, as in the case of the present Philip, and sometimes referred to as “Prince Consort”.
Now, if Elizabeth died, I suppose they would continue to call Philip “Prince”, even if he isn’t officially consorting anymore.
As Cecil has discussed here, there are Queens and there are Queens.
The late Queen Mother was a Queen Consort, by virtue of her marriage to King George VI. Elizabeth II, in contrast, is a Queen Regnant, that is a Queen in her own right.
As Cecil discusses, this does not work in reverse: Prince Philip is merely the Prince Consort, not King Consort.