If you wish to change setting part way through a term, you can do so. The funding will follow your child to their new provider. It is the responsibility of the provider your child is leaving to inform the Local Authority that you child has left/is leaving - otherwise they would be 'over-claiming' on their part. The new provider can then claim from when your child starts with them.
Parents are urged to check on the notice period of their provider before moving the child out of the provision.