I believe Arcade (no definite article) features on maps from as early as 1860 but not by name - only the buildings. Comparing the enumerators route along Glebe Row in the 1901 and 1911 census together with the 1939 register, I pinpoint it here (map from 1922):
My parents lived there 1935-39. The name "Arcade" doesn't appear on the 1901 census where everything on the east side of the road, with the exception of the Alma Inn and the Tankerville Arms, has the address "Glebe Row".
First in 1911 can we see that the six resident families are calling it "Arcade" - the majority without a number (only 2 and 6 give a number). The district enumerator, however, does not use the address "Arcade". He is still calling it Glebe Row. From this I draw the conclusion that Arcade is the familiar name used by the residents but not yet officially accepted.
As the residents are calling it "Arcade" I can only assume that the place has some features of an arcade and I believe that the 'alleyway' I've pointed out above was covered (hence the elongated x which appears on this and all other maps way back to 1860.
This position is also consistent with the 1939 register.