Alexandra Palace not Crystal Palace
Whoops. BBC TV didn't transmit from Crystal Palace in the 1930s. From the start of BBC TV in November 1936 until closedown, a couple of days from the outbreak of WW2 in Sept 1939, and then again from 1947 until the 1950s, the service was transmitted from Alexandra Palace in north London.
It was only in the 1950s that a new transmitter was built, on the site of the old Crystal Palace in south London, and services were moved there.
The Ally Pally mast is still there. It was used in a Doctor Who programme, the Idiot's Lantern, in 2006. The BBC used the space at Ally Pally for its studios from 1936 until the 1970s (when they were used for Open University programmes).