Personally I think they are right, _especially_ if there are no male refuges available. Which according to my cursory glances seems to be the case, at least in London[0].
[0]: https://www.standard.co.uk/news/crime/there-are-no-male-safe...
And reading your link it seems the government funding is clearly for both men and women:
> “Tackling domestic violence is a key priority in the Mayor’s Policing and Crime Plan. He has provided £2 million of funding for the Pan London Domestic Abuse Service – the biggest of its kind in London – which is open to men and women.
> “Through Survivors UK, the Mayor also supports male victims of rape and sexual abuse with funding to help them receive counselling through one-to-one support and advocacy support should they wish to report to the police and proceed through the criminal justice route.
Domestic violence shelters in the UK are almost entirely provided by charities.
I thought it was about government _funded_ refuges?
In July of 2018, while under austerity, the government gave 19M GBP to various charities who support domestic abuse survivors.[0]
Curiously, zero of those charities allow men to enter their shelters.[1][2]
[0]: https://www.gov.uk/government/news/19-million-fund-to-suppor...
[1]: https://localgiving.org/charity/safenet/project/janes-place/
[2]: http://www.cih.org/resources/PDF/presentations/arch2015/1Vic...
I think those people are wrong, especially if there are male refuges available.