If I had to summarize what Mrs. Dalloway is “about”, in a very brief form, I would say that it’s concerned with the way every person’s rough edges rub against each other and hurt the people around them. And that Clarissa, by her kindness, isn’t just generically nice. Her kindness is the lubricant that allows them to come together with less friction. This skill is particularly needed as society comes out of the trauma of a world war.
In that vein, there are two characters who are particularly rough edges. First there’s Peter Walsh, who has been puttering around the eastern colonies, apparently at mid-level government posts. He’s always falling in and out of love, has been divorced at least once, is in the process of breaking up another marriage. He un-self consciously brandishes his knife as a nervous habit.
Then there’s Dr. Bradshaw, who is a classic bully. His success at his job comes from breaking down mentally unwell people and molding them back into early-20th century England’s idea of a model citizen. He doesn’t so much seem to care about any of his patients as individuals, they’re all just the pigs that feed into the sausage machine of his medical practice. Coming to take Septimus away, he tosses Rezia aside like a rag doll. When the stress of the situation leads to Septimus’s suicide, he shrugs it off. That guy was a failure, not my methods.
I realized while reading this post from Alan Jacobs about post-WWI English society that this bumbling about abroad and brutal drive for conformity at home make Peter and Dr. Bradshaw Woolf’s stand-ins for the Empire and the homeland coming out of the first world war. Peter, capricious, fumbling, failing, aging, self-centered, causing harm almost more by accident than malice is the Empire. Dr. Bradshaw, arrogant, bullying, concerned only with conformity is England.