If you define stream of consciousness as the full emulation of a person’s thoughts and inner mental activity happening continuously in real time, and free indirect speech as akin to an inner monologue style of narration, then I would say based on the following excerpts that Ms. Dalloway does achieve authentic stream-of-consciousness in at least some of its passages:
For having lived in Westminster – how many years now? Over twenty – one feels even in the midst of the traffic, or waking at night, Clarissa was positive, a particular hush, or solemnity; an indescribable pause; a suspense (but that might be her heart, affected, they said, by influenza) before Big Ben strikes. There! Out it boomed. First a warning, musical; then the hour, irrevocable…
A sparrow perched on the railing opposite chirped Septimus, Septimus, four or five times over and went on, drawing its notes out, to sing freshly and piercingly in Greek words how there is no crime and, joined by another sparrow, they sang in voices prolonged and piercing in Greek words, from trees in the meadow of life beyond a river where the dead walk, how there is no death...
Stream of consciousness
- may be unpunctuated or unstructured to convey the fluid succession of one-thought-after-another
- portrays thinking by embodying it; is mimetic or performative as opposed to diegetic; shows, not tells
- may equally convey the inner events of consciousness such as thoughts as much as the percepts of consciousness, ie, witnessed, observed and experienced phenomena going on around the character from whose perspective the stream-of-consciousness comes
Free indirect speech
- may be a more conventional form of narration amounting to someone telling what is happening, in a story
- may resemble a monologue in that the narrator addresses a listener, implicitly
- Is disguised through stylistic conventions to mask its overtly diegetic, or story-telling, effect as happenstance, natural, or overheard.
Stream of consciousness enacts consciousness by being like it, whereas indirect speech conveys what a narrator would, while seeming or pretending that it is not really a narrator, is not talking to somebody, but is coming from within the story world.