The High Court also refused an appeal following the Duchess of Sussex's legal victory.
Judge describes application as "fishing expedition" that risked "high-profile" identification of "innocent individuals".
The ruling has been described by charity Mermaids as a "devastating blow" to trans young people.
The group said allowing women to have medical abortions at home went against the 1967 Abortion Act, which was to prevent "backstreet" abortions.
Senior judges rejected their claims of bias.
Krzysztof Pokorowski did not receive reminders because he was sleeping on the streets.
A third of staff were set to walk out.
Hearing ruled the one-year-old had been sexually abused, but that this did not cause her death.
The woman suffered a psychiatric injury following the birth of her child in 2012.
The child had been the subject of a protection order.