I recently went to a funeral that was contracted to a celebrant. I guess they do all the things religious organisations would normally manage. The Wikipedia page has a bit more info.
Edit: The funeral was managed by Tender Funerals. These are the services they offer. I'm not sure they consider themselves celebrants or if they have celebrants who work with them. Looks like I may have confused the two.
Edit 2:
Tender Funerals can help with the ceremony as little or as much as you require. There is no legal requirement for you to use a celebrant –anyone can take on this role. If you require this sort of assistance, we can help. We suggest you supply your own flowers and encourage you to create whatever you think would be the perfect goodbye for your person.