In this work, we propose theoretical and algorithmic-independent recovery conditions which guarantee the uniqueness of block sparse recovery in general dictionaries through a general mixed norm optimization problem. These conditions are derived using the proposed block uncertainty principles and block null space property, based on some newly defined characterizations of block spark, and (p, p)-block mutual incoherence. We show that there is improvement in the recovery condition when exploiting the block structure of the representation. In addition, the proposed recovery condition extends the similar results for block sparse setting by generalizing the criterion for determining the active blocks, generalizing the block sparse recovery condition, and relaxing some constraints on blocks such as linear independency of the columns.