The case of Isah, R (On the Application Of) v Secretary of State for the Home Department  EWCA Civ 268 concerned:
“the issue of whether a judge is permitted to order costs to be summarily assessed in a different court by a different judge or whether a summary assessment must be undertaken by the judge making the order for summary assessment, whether at the same time or at some point in the future.”
The Court of Appeal concluded:
“As [the Rules are] drafted, a summary assessment by its very nature must be carried out by the judge who heard the matter, whether immediately at the end of the hearing or thereafter.”
This conclusion might be thought to be unsurprising given the wording of PD 47 para.9.7:
“The court awarding costs cannot make an order for a summary assessment of costs by a costs officer. If a summary assessment of costs is appropriate but the court awarding costs is unable to do so on the day, the court may give directions as to a further hearing before the same judge.”
However, Coulson J had reached the opposite conclusion in the earlier decision of Transformers and Rectifiers Ltd v Needs Ltd  EWHC 1687 (TCC).
The issue has now been put beyond doubt.
Nevertheless, the Court of Appeal concluded that the judge making the order for summary assessment has significant flexibility as to how to undertake this assessment including in person, by means of a Teams hearing, by telephone or on paper.