I recently acquired a nice bound collection of 'The Lady's Magazine or Entertaining Companion for the Fair Sex, Appropriated solely to their Use and Amusement' for 1817. It isn't in terribly good condition, but contains all the illustrations which is unusual since there are fashion plates which were normally removed. The magazine for November is of course, almost entirely devoted to Princess Charlotte; Account of her Death, page 483, Authentic Memoir of, page 486, Observations on the Succession, page 496, Essay on the Princess's Death, with Characteristic Remarks, page 497, Claremont, description of, page 500, together with poetry: On the Death of her Royal Highness the Princess Charlotte, page 519, 520, All the People Mourning, page 521, and Fashion - Court Mourning, page 521. Under Chronicle, there is: Funeral of her Royal Highness the Princess Charlotte, page 523. Here is the frontispiece portrait of the Princess (cleaned up a lot by me due to print bleed-through):

The poetry is pretty awful - here is just a flavour:
'November
GLOOMY
November! doubly gloomy now;
For thou hast "cropp'd the fairest flower!"
With grief has made a nation bow,
And paralyz’d a nation’s power:
For thou hast a succession marr’d,
Which cheers a nation’s hope no more;
But Heaven has will’d, and man must guard
His lips from murm’ring, and adore.”
And so it goes on for another 13 or 14 stanzas. Yet another poem “On the Death of her Royal Highness the Princess Charlotte of Wales” is no better:
“Slow tolls the midnight bell. –ye frightful dreams,
Ye shades terrific- ye forbodings dire,
What mean ye?-What, at such a time as this,
When pleasure seems alive in every breast,
And Hope inspires us, what can damp our joys?
Relentless monster, Death, what has thou done?
For thou hast borne away the richest prize
The Universe could boast – our Princess falls!:
And so on and on. “On Hearing the Cathedral Bell Toll for the Death of the Princess Charlotte” is much the same (“....The pride, the hope of England is no more....”), as is “All the people mourning! A lament, for the Death of her Royal Highness the Princess Charlotte Augusta” (“.....Oh! we have lost a peerless gem!/We mourn in tribulation,/The Heiress to the Diadem!/The Darling of the nation!”....) – actually the last is shorter but pretty much the worst of a very poor albeit sincerely meant bunch. It is therefore interesting to note the change of mood for the details of ‘Court mourning’ which seem in both prosaic and detailed:
“Orders for the court’s going into mourning on Sunday the 9th inst. For her late Royal Highness the Princess Charlotte Augusta, daughter of his Royal Highness the Prince Regent, and consort of his Serene Highness the Prince Leopold of Saxe-Coburg, viz.-
The ladies to wear black bombazeens, plain muslin or long lawn, crape hoods, shamoy shoes and gloves, and crape fans.
Undress, dark Norwich crape.
The gentlemen to wear black cloth, without buttons on the sleeves or pockets, plain muslin, or long lawn cravats and weepers, shamoy shoes and gloves, crape hatbands, and black swords and buckles.
Undress, dark gray frocks.”
The theatres “have to boast of but little novelty during the present month, having been closed a great part of it from respect to her late R.H. the Princess charlotte. On the 21st, a Solem Dirge, with Mozart’s last Requiem was performed to a crowded audience. The House [the Theatre Royal, Drury Lane] presented a very sombre appearance. It was performed for the benefit of those Performers who have suffered by the shutting up of the house.....”
One of the most poignant of passages is very short, on “The King’s Health.....His Majesty has been generally in good health and tranquil spirits during the last month. His Majesty’s disorder has suffered no alteration.” George III was not told of Princess Charlotte’s death.
There is a long account of the funeral procession of Princess Charlotte, which was absolutely enormous and included not only members of the royal family and high status religious and political figures but members of the royal households, how far down it’s not entirely clear.
One can read many descriptions of how the nation was shocked at the death of Princess Charlotte, and concerned for the succession, but it is very immediate when you read it in a middlebrow sort of magazine such as this.