How would i relay to the services that I am taking a step back from her care?
Do social services already know that you are doing a lot of caring for your mum - usually that's the sort of thing that is asked during the care needs assessment. What level of care does your mum need at the moment, what things are you helping with during your visits? Is she currently vulnerable and at risk of harm without someone to help her with things like washing, cooking/eating/drinking, being appropriately clothed, preventing her from going out on her own and getting lost etc? If so, you should let social services know that your mum is vulnerable and at risk, and this might mean that the care needs assessment is prioritised as more urgent.
I think the other pressing issue at the moment is that your brother wants your mum out of the house and she will be homeless and reliant on social services to find her somewhere else to live. Has your brother given a date for when he wants her to leave? Are social services aware of your mum's housing situation? Depending on which area of Kent your mum lives in and which area of London you want to move her too then that may well result in being a more expensive option for the local authority so they will probably want to keep her within the same local authority area.
There's a lot going on here so I think it might be helpful for you to discuss the situation with the Dementia Support Line as they are very knowledgeable and helpful and will hopefully be able to provide you with a way forward:
If you need dementia support, we’re here for you. Get personalised information, support and advice by calling us on 0333 150 3456.
www.alzheimers.org.uk