Yes, the British love black dolls, too; and I love the ones they have manufactured throughout the years. I am partial to their hard plastic, ebony-complexioned dolls from the 1950s. Some have flirty (or follow-me) eyes that enhance their character. The addition of astrakhan wigs to mimic the naturally dense texture of "black" hair, and broader facial features add to their character. Images, captions, and links follow:
Pedigree Delite toddler (can be dressed as a boy or girl), made of hard plastic during the 1950s; has astrakhan wig. This head sculpt was also used for babies (male and female) with bent legs.
Baby Cara, Caleb, Sasha, Cora, and Gregor ~ Dolls by Sasha Morgenthaler, Made in England during the 1970s
Amanda Jane Ltd, the manufacturer of Amanda Jane and Amanda Jane Baby from 1977 and ca. 1975, made dolls from 1952 through 2007.
Visit the eBay store of Nubidollz, an England-based doll merchant who specializes in black and ethnic dolls.
Additional black dolls from England and other black dolls are discussed here by Sue Brewer, publisher of Doll Showcase Magazine and author of Tiny Tears and First Love: A Celebration of Two Classic Baby Dolls.
Not dolls, but these black greeting cards designed by a talented artist in the United Kingdom (JWGreetings), might interest you.