From an Arsenal fan site:
http://www.fl.net.au/~steve/didyou.htm
"Arsenal were also the FIRST team to be covered by television cameras. On the 16th of September 1937 the cameras rolled for the first time for a friendly match arranged specially for the occasion between Arsenal first and Arsenal reserve teams."
The page also lists a number of other Arsenal radio and television firsts.
Arsenal's own website says that the first match was televised in I]1927[/I] but this can't be correct. They must mean radio:
http://www.arsenal.com/article.asp?thisNav=The+Club&article=363272&Title=Arsenal's+A+to+Z
I read recently that 20,000 television sets had been sold in Britain by the start of the war.