I'm sure OP won't mind a slight derailing.
Very very few babies are "relinquished" these days and certainly not on the grounds simply that they are from single mothers.
Off the top of my head, children are removed very young (ie at birth or soon afterwards) if there is continuing drug or alcohol abuse or significant neglect and/or abuse either of the baby or of older siblings.
Older children are removed due to actual harm or significant risk of actual harm.
Very young babies might go into a concurrent planning foster care ie foster carers will be first choice to adopt if the baby cannot be returned to birth parents and have to facilitate contact with birth parents whilst the child is being fostered. Or might go into foster care. I'm not sure how you would differentiate "languishing" from "being"! The vast majority of children in care have no adoption plan so will remain in foster care either until they age out or until they are able to return to family.
There is a focus on speeding up the process once a plan for adoption has been made to try to minimise the temporary care a child goes through but inevitably some children are harder to place than others - more significant abuse, larger sibling groups, specific needs etc
As far as I know care homes tend to be used for older children where there is no plan for adoption although obviously they are fostered too.
Adoption in the UK is not as clear as "closed" or "open", some degree of contact is nearly always encouraged eg annual letterbox contact as a minimum but there may be security issues, threats made against adoptive parents etc that have to be taken into account as well as what is in the childs best interests.
I know parents on this board who maintain significant contact with birth parent and siblings, those who maintain letter box contact (despite in many cases never getting an reply) and those who have no contact at all - where it simply isn't possible.