Please help! How to get help for my family? Uk

Hi I'm needing help for my mother and dad and younger brothers who live with her.
She's making their life's miserable. She is undiagnosed but definitely needs to be but refuses.. It's been suggested by us and others in the past and she has gone absolutely flipping mental at it before... And will again. She's an emotional blackmailer with pretty paranoid ideas and fears.. She's accused them of hurting her and bullying her... Another of her recent thing is on of her old friends whom tried to tell her she needed help who my mum then cut out her life and told her she never wanted to see her again... Well a few weeks a go this woman came for a coffee at their house after my mum and her had some phone calls.. She had some birthday presents for my brothers. Well it went well they had coffee said they'll do it again.. Now she's gone bk to saying she never wants to see her again, how she's been calling and won't leave her alone.. My dad doesn't believe this has happened at all..

She's recently been diagnosed with MS and has learning difficulties.. She been given a emergency call button for incase she falls and can't get up.. Well that's not going to happen but she's been given it whoever partially to keep her happy and partially for when/if the MS progresses to that stage..
So last month dad and brothers were trying to talk to her about the need for a social worker (she told the social work dept she didn't need them) she pushed "the emergency button" started hysterically crying down the phone telling them her family were trying to hurt her and we're bullying her!

Trouble is she would never ever go to a doctors about it.. There's no reason to as far as she's concerned.

She's pretty much always been like this... For as long as I can remember anyway... Well enoughs enough! My dad called me tonight in tears asking me what to do, I've had my brothers in tears on the phone in the last month. I've been in tears...

I love my family and I love my mum but if she doesn't start getting help she's going to lose us! I don't live anywhere near them (thank god) But my brothers are both 16 and could both technically leave home... Give a few years they will (they wouldn't now, she's messed their heads to much with her blackmail) but they will, and so they should. Their intelligent boys and could easily go to uni in the future.. when they do move out my dad has said, as it is now he wouldn't stay there on his own!

I don't want this! I want them to find a solution. I don't want my mum left on her own, God know what she'd do... I want to get her the help she won't. No. we need to get her help!

Where do we go? Who do I call?