If you have chosen not to have the hospital arrange a funeral for your baby, you could contact a funeral director to assist you. A few crematoria will accept cremations through funeral directors only. The hospital staff may be able to give you the contact details of local funeral directors who specialise in funerals for babies. You can also find information in the Good Funeral Guide http://www.goodfuneralguide.co.uk or the National Association of Funeral Directors (NAFD) website at http://www.nafd.org.uk
It is important to make sure that the funeral director you choose is a member of a professional body such as NAFD. The funeral director will ask you to sign a form allowing them to collect your baby from the hospital mortuary and they can usually organise the other paperwork that is required.