"...so won't give permission for the name change."
An adult over the age of 18 doesn't need anybody else's permission to change their name.
Is this a child under 18 that you're talking about?
If a child is 16 or 17 then they can make an unenrolled deed by themself.
For an enrolled deed for a child under 18 then everybody (typically both parents) with parental responsibility must agree in writing.
However, all of that is just for a child. If this person is an adult then they do not need anybody else's permission. Once the child turns 18 they no longer require permission.
"(as it would be dangerous for the person in question to go down the enrolled route due to abuse)"
The government website suggests that you include this information in your application:
"A public record of your name change and your address will be published in The Gazette. If you have a strong reason why your details should not be published, explain why in your application. The judge may agree to only publish your first name or surname."