That episode has a lot of English stereotypes, and they can go back and forth from entertaining to a little trying. I kind of think Honor Blackman was told to play Lilly as a pretty stereotyped English socialite, and that can wear a little thin.
I have to agree with the second part of the original post. Beth Chadwick was made an overnight success in her own mind after killing her brother. She took that alleged success and ran with it fast and furious. Changing everything about her style, or hair, or dress, and her way of running the company. She was rude and crude to her mother, and had she have married Peter, she would definitely have worn the pants in that relationship.