Here, in Australia, we call it Yum Cha. Most of the names of the dishes are the same, except a certain dish is called a dim sim - the SIU MAI.
Ah, wikipedia to the rescue. en.wikipedia.org/.../Yum_cha
"In the U.S. and UK, the phrase dim sum is often used in place of yum cha; in Cantonese, dim sum (點心) refers to the wide range of small dishes, whereas yum cha, or "drinking tea", refers to the entire meal."