We have investigated the magnetization properties and flux dynamics of superconducting Cu$_x$TiSe$_2$ single crystals within wide range of copper concentrations. We find that the superconducting anisotropy is low and independent on copper concentration ($gammasim1.7$), except in the case of strongly underdoped samples ($xleq0.06$) that show a gradual increase in anisotropy to $gammasim1.9$. The vortex phase diagram in this material is characterized by broad region of vortex liquid phase that is unusual for such low-$T_c$ superconductor with low anisotropy. Below the irreversibility line the vortex solid state supports relatively low critical current densities as compared to the depairing current limit ($J_c/J_0sim10^{-7}$). All this points out that local fluctuations in copper concentration have little effect on bulk pinning properties in this system.
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