I dunno if they will give you UK legal advice, but they can tell you whether they are a "Safe Harbour" firm.
As I said, though, since you're not actually transferring the personal information to DreamHost as a corporate entity but rather transferring them to DreamHost facilities for some express purpose for which there is a legitimate business need that the parties have agreed to, DreamHost wouldn't need to be a safe harbor firm.
The main question is what you're doing with this personal information and why do you need to upload them to your web host?
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