Hi Honeybun,
I contacted a reliable source and received the following reply.
The present practice of the Church of England, while much is left to the discretion of the minister, says No. Funeral Services are published in a book called 'Pastoral Services' and on pages 316-7 there is a 'Theological Note on the Funeral of a Child Dying near the Time of Birth' which encourages clergy to provide a sensitively adapted funeral service for stillbirths or children who die within hours or days of being born. It includes the phrase 'You cannnot baptize someone who is dead', and gives reasons. I do not know about other denominations, but I notice that the Roman Catholic church has now stopped speaking of limbo as the place where unbaptised babies go, and leaves their fate to God's mercy.
Best Wishes,
Christopher