Criminal cases in England and Wales always start in a magistrate's court. The judge in this case, Vanessa Baraitser, is listed [1] as a "District judge (magistrates’ courts)" - despite the article describing her as "Magistrate Baraitser". District Judges are full-time members of the judiciary, even though they sit in a magistrate's court [2].
Obviously, the case will be considered by other judges on appeal.
Also, extradition proceedings don't follow standard criminal procedure.
See s77(1) of the Extradition Act 2003...
> In England and Wales, at the extradition hearing the appropriate judge has the same powers (as nearly as may be) as a magistrates' court would have if the proceedings were the summary trial of an information against the person whose extradition is requested.
(A summary trial is a trial for a low-level offence - in the US, the equivalent would be a misdemenor. "An information" is a slightly quaint wording for what is basically equivalent to an indictment, except it isn't an indictment because a summary offence isn't indictable.)
In the magistrates' court, you either have a bench of three lay magistrates, or a district judge. More serious issues, including almost all but the least contentious extradition hearings, are likely to be heard by a DJ rather than a lay bench, since a DJ has worked in legal practice in a way a lay magistrate hasn't.
Criminal cases in England and Wales always start in a magistrate's court. The judge in this case, Vanessa Baraitser, is listed [1] as a "District judge (magistrates’ courts)" - despite the article describing her as "Magistrate Baraitser". District Judges are full-time members of the judiciary, even though they sit in a magistrate's court [2].
Obviously, the case will be considered by other judges on appeal.
[1] https://www.judiciary.uk/about-the-judiciary/who-are-the-jud...
[2] https://www.judiciary.uk/about-the-judiciary/who-are-the-jud...
Edit: added "in England and Wales"