As I mentioned in the previous shot, we can see a sign at the front of Piccadilly Arcade that says Santa Maria Novella, established 1612.

That's a name which is more commonly associated with city of Firenze in Italia. And that's not surprising because according to the company's own website it was founded not here in London, but rather in Firenze.

The shop is a pharmacy which was established by Dominican friars. (Though I believe that this specific shop sells perfumes rather than medicines.) It's not entirely clear when this London incarnation of the shop first appeared. There is also something a little bit odd in the arcade's description of the store. It acknowledges that the pharmacy was established by Dominican friars, but then says that it was "continued by the family up to this day".

And how, exactly, did by-definition celibate friars have a family? (OK, THEORETICALLY celibate, at least.)

According to the company's website (which is in Italian), what would eventually become this pharmacy actually began in the 13th century when the friars arrived in Firenze. It remained in their control up until 1871, aside from a brief period during the Napoleonic era when the assets of the monasteries were confiscated by the state. (One of the friars bought the assets while the area was under French control, and then sold them back to the order after Napoleon's defeat.)

The claimed commencement date of 1612 was in fact the year in which the pharmacy began selling to the public as opposed to providing products for patrons.
Between 1871 and 1991:
"La proprietà della spezieria passa alla famiglia Stefani, discendenti di Cesare Augusto nipote di Fra’ Damiano Beni."

Or to translate, ownership of the pharmacy passed to a family named Stefani, who are descended from Caesar Augustus. A rather interesting claim, since Augustus had only one child (ignoring adoptions like that of Tiberius), a daughter, who did admittedly have some children. However it is generally accepted that the Julio Claudian dynasty died out when Nero did so that claim may be, shall we say, "poetic" in nature.
How long has this pharmacy been here? Well, obviously not before 1910 since that's when the arcade was constructed; whether there was a branch here before that or whether it's a relatively new outpost is something that I haven't really been able to find out.

I rather suspect that you would be paying a premium for the history of the products that you buy here. Nonetheless, it might be interesting to take a look if you're in the neighbourhood.