Independent Placements
There are many organisations claiming to help people, who have been unable to adopt a child through a Local Authority or Adoption Agency. It has been illegal for many years to arrange an adoption for money or any other incentive. There are criminal offences punishable by a fine and imprisonment, for arranging an adoption other than through an approved agency.
It's not illegal to place a child for adoption with a relative, but the adoption will still be subject to all the other requirements set out on this site, in particular close investigation by Social Services and the courts.
It's also not illegal to place a child with someone, purely to look after the child, if adoption was never thought of at the time. Indeed, Social Services are required to look at a child's wider family as possible carers rather than take the child into care. A temporary arrangement may become a permanent one, and adoption is one of the legal options long-term.