Because the courts are independent, the House has agreed that, subject to the discretion of the Speakers, Members should not refer to matters which are before the UK courts (including inquests).
In addition, MPs should not write to a judge in terms that might appear to be using their status as an MP to attempt to interfere with the process of justice or with judicial independence. They can give character references if they know the person concerned and are asked to do so but as a general rule they should not write to a judge about an individual case. This applies to any judge, not just the judge hearing the case in question.