  Supernova remnants are believed to be the main sources of galactic Cosmic
Rays (CR). Within this framework, particles are accelerated at supernova
remnant shocks and then released in the interstellar medium. The mechanism
through which CRs are released and the way in which they propagate still remain
open issues. The main difficulty is the high non-linearity of the problem: CRs
themselves excite the magnetic turbulence that confines them close to their
sources. We solve numerically the coupled differential equations describing the
evolution in space and time of the escaping particles and of the waves
generated through the CR streaming instability. The warm ionized and warm
neutral phases of the interstellar medium are considered. These phases occupy
the largest fraction of the disc volume, where most supernovae explode, and are
characterised by the significant presence of neutral particles. The friction
between those neutrals and ions results in a very effective wave damping
mechanism. It is found that streaming instability affects the propagation of
CRs even in the presence of ion-neutral friction. The diffusion coefficient can
be suppressed by more than a factor of $\sim 2$ over a region of few tens of pc
around the remnant. The suppression increases for smaller distances. The
propagation of $\approx 10$ GeV particles is affected for several tens of
kiloyears after escape, while $\approx 1$ TeV particles are affected for few
kiloyears. This might have a great impact on the interpretation of gamma-ray
observations of molecular clouds located in the vicinity of supernova remnants.
