Government officials are expected to argue that the number of abortions performed for conditions like club foot and cleft palate must remain confidential.
Up until 2002 such data were published, but ministers stopped the practice if fewer than 10 cases were involved, saying it risked identifying the women or doctors involved.
However, the ProLife Alliance challenged this stance in 2005 and requested the release of the figures under the Freedom of Information Act.
The Information Commissioner ruled that the details of abortions must be disclosed, but the Department of Health refused and appealed against the commissioner's decision.
Now an appeal panel will listen to experts who believe the numbers must remain confidential. An agreement has been reached for part of the hearing to be heard in private.
Rules state that abortions under category E, which relates to disability, can be performed up until birth as long as two doctors agree on the procedure.
There is no list exempting certain conditions such as cleft palate or club foot.
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