I've just discovered that those big (often black) plums grown in warmer climates are japanese plums, P salicina, though many of the varieties grown outside the far east originate in California or Australia. Now it turns out that there are some P salicina sold for cultivation in this country. http://www.readsnursery.co.uk/cultur...lum-trees.html
They are the only nursery in the country listed on RHS plant finder with P salicina. But one or two others do seem to be selling eg "Methley" but describing it as P domestica.
Since Reads is in Norfolk, you may have a chance! They are very early flowering though. Elsewhere on the web I read they do need protection to keep the fruit.
http://www.fruitforum.net/poor-mans-fruit-walls.htm