I dont think there are any "shelters" in the UK, but maybe in the States where there are shelters, they are privately funded.
Most refuges in the UK survive on housing benefit, short term project funding or specialist staff, and some charity funding usually for child services.
And if lucky, their local council will fund them to provide support for women escaping male violence, but that council could decide it is cheaper to give the funding to a genric service homelessness service.
Even in Brighton a women's DV service had their funding taken away (and they are trans inclusive!) and it was given to a generic housing service.
By keeping an eye out, it means looking at the web site of your local council, reading budgets (groan), lobbying local councillors and finding out how the refuge itself thinks it is best to campaign. eg forming a local campaign group.