This magnificent building on the corner of York Street and Arragon Road in Twickenham has a surprisingly poor internet trail. Our first thought was that it might have been a telephone exchange but I rejected that because it isn't ugly enough* (or at all really).
Further inspection revealed some really lovely reliefs depicting electricity which means I am inclined to accept Edith's assertion (on the rather good Edith's Streets blog) that it used to belong to the South Eastern Electricity Board. It definitely now belongs to Richmond upon Thames Council.
*I have never seen an attractive telephone exchange. (Any exceptions gratefully received.)