Hi poorbear,
Refuge would not normally place you in one in your home town for your safety reasons, so if you want to move away and are prepared to move as far away as possible this should technically be easier to get a place for you. Many women like to stay near to where they live for work reasons or family and the thought of moving too far is the ‘deal breaker’ for them going to refuge.
I think if you tell them you are willing to move anywhere it helps them to see where they have vacancies and they can offer you an area where there is a vacancy.