If you remember the Ritz / Essoldo cinema was then you will know where Davies St. was - because it was directly underneath it. The cinema was bounded by Kendal St, Wilton St, Claughton Rd and Oliver St. So Davies St must have been demolished sometime before 1937, when the Ritz was built and opened.
Just for information, it was bombed during the war and rebuilt inside as the front was largely undamaged.
In 1947 it held a Royal film performance - seen here on YouTube https://www.youtube.com/watch?v=zZCIquLviMk.
It converted to a bingo hall in 1966, swapping name and function with the Essoldo over the road in Conway St. Sometime in 1996 or just after, it was demolished (shortly after the flyover was demolished) and became a car park.