In the majority of instances, planning permission is not required to install a patio awning on the rear of a residential property, as these fall under permitted development rights. There are some exceptions however, including where your property is located in a conservation, green belt or AONB (area of outstanding natural beauty), your property is listed and where permitted development rights have been removed (usually in historic locations to protect the character of an area). Your awning should not extend over or encroach your neighbours boundary and additionally must not be positioned so that rainwater will run off or drain onto your neighbours boundary either.
As every local authority regulations vary, there is no one rule for all, so if you are unsure it is always recommended to check with the local authority.