How acceptable is it to submit a paper where most of the references are written by the same group of authors? I am preparing a conference paper. I have been looking for references for a specific topic related to my research. I have not found any that were not written by current/former members or my research lab. 
How common is it and how acceptable is it to submit a paper where most or all of the references were written by the same group of authors?

In other words, my adviser is an author for most/all of them with a subset of his students.
If your work is either very new or very esoteric, then I don't see that this would be unusual. However, for a more general topic there might be some issues. When I finished my dissertation the topic wasn't new, but it was very esoteric. I knew of only two universities in the world where there was interest in the problem and only about a half dozen people interested. All were either professors or students at those two institutions. 

Research is very specialized and often balkanized. So, if there are, in fact, few or no other papers then the situation is determined by the facts and is therefore acceptable. Publishing may spread interest and the "problem", if any, will disappear in time. 

Make sure your search was thorough, of course. It wouldn't do to be informed of a wide body of work that you missed.