Thank you Tees, Roobarb and Rhododendron for your contributions, but I agree with Chempat. As can be seen from the 1930 map that he posted, there is no Levenvale Street adjacent to Brookbank Ave., nor anywhere else in Redcar.
Furthermore, if you look at the initial "S" in "September" (second last column) it is clear that the initial letter in "Hut" is not an "S" as in "Street".
On reflection I think that "Levenvale Hut" may have been the name of the house in Brookbank Avenue. Levenvale / Vale of Leven appears to be in Scotland. Could "hut" be a Lallans word for "house"? I am imagining the owner of the house as being someone who either came from Levenvale or had very pleasant memories of (holidays?) spent there.