Quoting from the judgment:
"Nobody in this country is sent to prison for contempt of court "in secret"."
and
"Had I sent her to prison in private my decision would have been unlawful and the Court of Appeal would have had the power to set it aside. I, myself, have been very critical of a judge who sentenced a contemnor without hearing mitigation and without going into open court to do so; see the case of Hammerton v Hammerton [2007] EWCA Civ 248, [2007] 2 FLR 133, in which the order of the judge was set aside.
There is, of course, an automatic right of appeal against a committal order. Permission to appeal is not required - see CPR rule 52.3(1)(a)(i). Added to which, of course, the Court of Appeal sits in public."
Which admits that is has happened.
In other words additionally it requires an appeal. I will check a number of the cases where people have been jailed in secret (including suspended sentences) to find out what exactly has happened. It is important to remember that the system resists providing documents for appeals.
the underlying problem, however, is that secret trials are unreliable.