This description of the clocks on Harley Street emphasizes the feeling in the novel that time is constantly trudging on, almost terrorizing its characters while also strangely bringing everyone together, since everybody experiences the effects of time, even if their lives don’t overlap at all:
Shredding and slicing, dividing and subdividing, the clocks of Harley Street nibbled at the June day, counselled submission, upheld authority, and pointed out in chorus the supreme advantages of a sense of proportion, until the mound of time was so far diminished that a commercial clock, suspended above a shop in Oxford Street, announced, genially and fraternally, [...] that it was half-past one.
The phrases "shredding and slicing, dividing and subdividing" and "nibbled at the June day" describe the "clocks of Harley Street" as if they have some sort of agency, making it seem as if they're actively eating away the day. In fact, these words suggest that time is being devoured, thus leading to an odd sense of urgency and underlining the fact that it's impossible to stop the inevitable passage of time.
More importantly, though, this passage about clocks and time occurs after Lucrezia and Septimus leave Sir William Bradshaw's office. Bradshaw has just spoken at length to them about the value of having "proportion" in life, which he thinks is capable of fixing mental health problems like the ones Septimus is experiencing. And yet, he is described as a domineering, somewhat callous man who overpowers and "devour[s]" his patients as he tends to them. Neither Lucrezia nor Septimus like him, and it's clear that the ominous description of the clocks in the street is somehow tied to their feelings about Bradshaw—both the clocks and Bradshaw are committed to order and regimentation. This passage thus personifies the clocks by suggesting that they point out "the supreme advantages of a sense of proportion," making it clear that the clocks have come to stand for Sir William Bradshaw himself.
