want to move out but benficts would be effected

I currently live with my mum we share the house and am on benfiets due to my disabitlys and problems. she is my carer. and mum relys on the money to keep paying for bills for the house and other stuff liek foods clothes. she been a carer for me and my grandma most of her life. so she lacks work experince she recently trying to get a job part time with her being over 60 she not had much luck. and with my bf i would like to move out with my boyfriend. Only worry is my benficts would be stopped and that we would have to relie on his income which wont be enough bewtWeen two people. plus most places of rent dont do bencifts. want to know if there a way to keep some of my benficts while living with him and him doing full time a food place low wage. His parents always put the pressure on. with being together 3 years we should be living together by now. but with finenal problem its put us on hold abit.