Page 87 of the 25th edition of the London Zoo guide book from 1928 featuring sparse information about the Thylacine kept there at the time, the subsequent guide books show alternate images
This is an earlier Thylacine, probably in the old kangaroo House so not actually the NMH in this photo .. Only the last Thylacine at London Zoo lived in the NMH Afaik.
The three photos from the three guide books I have showing Thylacines all show the same little courtyard with the bricks and doors behind so you are probably correct.
@Daubentoniidae The North Mammal House was a similarly designed building so one could easily double for the other in a photo- though the wooden door and boarding was only in the Kangaroo house. Also I know this isn't the last Thylacine that died in 1931, which was the only one that lived in the NMH.