In Pride and Prejudice, how is London presented in Chapters 24-28 and how does Lady Catherine behave in Chapters 35-42?

London really isn't presented; there are a few mentions, a few lines about one area being more affluent than another and even mention of specific places, but London itself is not presented or described outside of the fact that everyone wishes to visit there. The following quotes are the closest I could find;

"And that is quite impossible; for he is now in the custody of his friend, and Mr. Darcy would no more suffer him to call on Jane in such a part of London—! My dear aunt, how could you think of it? Mr. Darcy may perhaps have heard of such a place as Gracechurch Street, but he would hardly think a month's ablution enough to cleanse him from its impurities, were he once to enter it; and depend upon it, Mr. Bingley never stirs without him."

"The improvement of spending a night in London was added in time, and the plan became perfect as plan could be." (Chapter 27)

The Parsonage (Chapter 28)

"At length the Parsonage was discernable. The garden sloping to the road, the house standing in it, the green pales and the laurel hedge, everything declared that they were arriving. Mr. Collins and Charlotte appeared at the door, and the carriage stopped at a small gate, which led by a short gravel walk to the house, amidst the nods and smiles of the whole party. In a moment they were all out of the chaise, rejoicing at the sight of each other. Mrs. Collins welcomed her friend with the liveliest pleasure, and Elizabeth was more and more satisfied with coming, when she found herself so affectionately received. She saw instantly that her cousin's manners were not altered by his marriage; his formal civility was just what it had been, and he detained her some minutes at the gate to hear and satisfy his enquiries after all her family. They were then, with no other delay than his pointing out the neatness of the entrance, taken into the house; and as soon as they were in the parlour, he welcomed them a second time with ostentatious formality to his humble abode, and punctually repeated all his wife's offers of refreshment."

Lady Catherine behaves completely out of character; she asks Elizabeth to stay with her............ that's a change of heart. She appears to be genuinely sorry they're leaving and even sends a servant with them so they won't be traveling alone. She has something up her sleeve!

"Why, at that rate, you will have been here only six weeks. I expected you to stay two months. I told Mrs. Collins so before you came. There can be no occasion for your going so soon. Mrs. Bennet could certainly spare you for another fortnight." (Chapter 37)

"Mrs. Collins, you must send a servant with them. You know I always speak my mind, and I cannot bear the idea of two young women travelling post by themselves. It is highly improper. You must contrive to send somebody. I have the greatest dislike in the world to that sort of thing.—Young women should always be properly guarded and attended, according to their situation in life. When my niece Georgiana went to Ramsgate last summer, I made a point of her having two men servants go with her.—Miss Darcy, the daughter of Mr. Darcy of Pemberley, and Lady Anne, could not have appeared with propriety in a different manner.—I am excessively attentive to all those things. You must send John with the young ladies, Mrs. Collins. I am glad it occurred to me to mention it; for it would really be discreditable to you to let them go alone." (Chapter 37)

Lady Catherine had many other questions to ask respecting their journey, and as she did not answer them all herself, attention was necessary, which Elizabeth believed to be lucky for her, or, with a mind so occupied, she might have forgotten where she was. Reflection must be reserved for solitary hours; whenever she was alone, she gave way to it as the greatest relief; and not a day went by without a solitary walk, in which she might indulge in all the delight of unpleasant recollections. (Chapter 37)