Migration ESA to UC

I am about to move boroughs within London and so change housing associations and understand that my old Housing Benefit claim will close and I should then claim UC. I receive legacy benefit ESA and am in the support group but within that I receive £90.50 living expenses and £47.70 because I am in the support group but also £81.50 extra money because I am severely disabled and £20.85 extra money because of the disability income guarantee. I realise that I am extremely fortunate but will I lose the £80.50 and £20.85 by moving ? I’m autistic and dyslexic and I’ve tried to work through the forum answers and online chats but very confused. Is there any way I can apply for/force a managed migration ? I understand that I would keep the disability premiums if that were the case. I also receive PIP having been migrated from DLA two years ago. Should I apply to change to UC now before I move so I don’t enter the UC assessment period ? I expect the move to happen within 6/8 weeks which is to be nearer the hospitals I use but am very anxious at the effect on the benefits