There are 3 types of pronunciation of "did you" I've heard, /di ju:/, /di dʒju:/ and /di dju:/.
I've never heard anyone pronounce did you as /di ju:/. It might happen in fast speech but you should definitely not aim for it.
/di dʒju:/ is the pronunciation of did you in normal/ casual speech.
In did you, sometimes the /d/ of did and /j/ (y) of you assimilate to /dʒ/. The process is called assimilation.
It's because when you articulate /j/ immediately after /d/, the place of articulation becomes very similar to that of /dʒ/ so it sounds like /dʒ/.
See Yod-coalescence
And /di dju:/ is the normal pronunciation of did you (without assimilation).
When a speaker, usually an American, doesn't pronounce the second 'd', that would be /di ju:/.
It's not restricted to AmE or BrE. It can happen in all varieties of English. And once again, eliding the d from did is very informal and I've never heard it.