Who sends Jane Bennet a letter from London in Pride and Prejudice by Jane Austen?
In Chapter 26, Volume II, Jane goes to London to her Aunt and Uncle Gardner to emotionally recover from her sorrow at the departure of Bingley from Netherfield. In Chapter 39, V. II, Jane and Elizabeth, who had been in Kent at Rosings, leave London together to return to Longbourn. The Gardners remain in London but the only letters they send to Netherfield are to Elizabeth and then to Mr. Bennet. Once the touring party reaches Derbyshire, letters from Jane go to Elizabeth but none go to Jane from London.
The letter you must be thinking of is a letter quietly mentioned at the end of the novel in Chapter XVIII (60) of Volume 3. Once Darcy and Elizabeth are engaged, immediately following Jane's engagement to Bingley, Caroline Bingley has nothing to lose but much to gain by civility and kindly, sisterly acceptance of Jane. Consequently, she sends a letter from London to Jane at Longbourn expresses these very appropriate and practical sentiments. So Jane Bennet receives a letter from London from Miss Caroline Bingley, Mr. Bingley's sister, whose hopes of marrying Mr. Darcy are vanished.
[Miss Bingley] wrote even to Jane on the occasion, to express her delight, and repeat all her former professions of regard. Jane was not deceived, but she was affected; and though feeling no reliance on her, could not help writing her a much kinder answer than she knew was deserved. (XVIII (60), V. III)
You might also be thinking of a letter that arrives for Jane just after the Bingleys and Darcy have vacated Netherfield for London. Jane is only informed of Mr. Bingley's departure via this letter, sent to her by his sister, Caroline Bingley, in Chapter 21. In the note Caroline implies that the whole party will remain in town indefinitely. She also insinuates an impending match between Bingley and Georgiana, Mr. Darcy's young sister.
My brother admires her greatly already; he will have frequent opportunity now of seeing her on the most intimate footing; her relations all wish the connection as much as his own, and a sister's partiality is not misleading me, I think, when I call Charles most capable of engaging any woman's heart.
Needless to say, the news devastates Jane, who had every hope for a match with Mr. Bingley herself. She is too naive to see Caroline's meddling behind the departure, but Elizabeth is not.
Because of the important nature of this letter and the timing of its arrival--some time after the party has quit Netherfield but before they have arrived in London--this may also be the letter to Jane you were thinking of.