I've only recently discovered this excellent resource site - Pathe newsreels are archived and available to watch online. Whilst doing a random search for 'calypso' on the site (as you do) I came up with this little gem and what do you know, London's Chinatown is featured straight away! The calypso nightclub is in Reel 2 and well worth checking out (great jiving moves from the customers). It is a little like a round the world tour, designed to show the capital as a multicultural entertainment zone where you can eat chop suey followed by Russian vodka and Calypso Be-Bop dancing.
After the war rationing was still in place and this is mentioned in the film - rice was not available for instance. I love the line about the pandas in the zoo being the only ones who could get real bamboo shoots!
I have searched for further info on the Chinese restaurant Leyons but not come up with anything so far. It looks like it opened in the late 1930s because of its wonderful Art Deco style.