I am assuming that you are a family friend of a family where a child has been removed from parents and is in the care of the LA. Is that right?
If that is the case, then you need to contact the LA who has the parental responsibility for the child if he/she has been removed from birthparents. It is difficult to answer with so little information, but when a child is removed from parents, they are in some cases placed with foster carers initially, though some can be placed directly with relatives/friends.
There will be numerous assessments done on the parents to see if there is any way the child can remain with them. If the LA have evidence that this is not safe for the child, then they must plan the child's future. They do have a duty to see whether the child can be placed with the extended family or close friend, before looking for other foster carers/adoptors.
The best thing to do is to contact the child's social worker (the birthparents will know who it is) and say that you are interested in being considered to care for the child. That is the very first step. Much will depend on you, your circumstances, the child, or children, your friendship with the family etc etc.
I would just add that if and when the time does come that you are being seriously considered to care for this child/ren on a permanent basis, then the Residence Order is not the best Order to apply for. The best Order in these cases is Special Guardianship Order, as there are Regulations attached to this Order that makes the child's future more secure.
Residence Orders are really for cases where the birthparents are separated and are in a battle about who cares for their children.
If you can give more info I might be able to help more. You can PM me if necessary.