She has a British accent.
Not so much anymore, since she's lived in the US for 20 years. Here's a recent clip
of her where her accent sounds like a mix of American and her original Cockney and maybe a few other things. Of course, as an actress, Sirtis is capable of doing multiple accents; the "British accent" she usually uses onscreen is more upper-class than her native East End accent, and of course Troi's accent was originally a made-up blend of various Mediterranean and Eastern European influences that evolved to become more mid-Atlantic by the end of the series. (If anyone doesn't know, "mid-Atlantic" refers to an accent that's indeterminately between English and American, sounding English to American ears and vice-versa; it's often used by supposedly English characters in American films and shows. In fact, Sirtis considers Troi's later accent to have been "American."
) And she's done a full-blown American accent in various parts, like Margot in Gargoyles