Hello everbody,
The only destroyer number D 01, that I could find, was the "Scott" class destroyer MONTROSE built by Hawthorn Leslie (Hepburn) and launched 10th June, 1918. It was renumbered I 01 in 1940. She was sold to Hughes Bolckow, arrived Blyth 31/1/46 for scrapping. The number on the funnel could be the Flotilla number, eg 23 = 23rd Destroyer Flotilla. Though I think that this was only done after WW 2. Could the destroyer be a post war one?
Hope that helps some,
Bruce.