Yes, it sounds like this was inappropriate but possibly not illegal. Normally the strongest sanction the judge could take here would be to find them in contempt of court, but he let them off with a warning/admonishment which also seems fine.
> IPT secretary Susan Cobb wrote back to say: "It was inappropriate for your staff to seek to intervene in ongoing legal proceedings..."
> Lord Justice Singh told the room: "The tribunal's secretary acted entirely appropriately in responding the way she did and by drawing these matters to my attention. In March 2019, it was recognised that the direct communication was inappropriate."