CPR 47.2 is very clear that any Detailed Assessment is not stayed pending an Appeal unless the Court otherwise Orders. In a recent case Mrs Justice Slade decided in Axton & another v G E Money Mortgages Limited & another  EWHC 1343 (QB) that similar considerations should apply on Summary Assessments.
The Judgment sets out that Summary Assessments should take place at the conclusion of a hearing which has lasted not more than a day unless there was good reason not to do so. Mrs Justice Slade was anxious to make it clear that the use of a threatened appeal to potentially defer quantification of the liability for costs was not something which she would wish to encourage. Interestingly, she went on to note the major advantage of Summary Assessment is that it is to be undertaken by the Judge who has dealt with the hearing. In Transformers and Rectifiers Ltd v Needs Ltd  EWHC 1687 (TCC), there is a comment by Mr Justice Coulson who has made it plain that Judges can Summarily Assess costs even if they did not make the Order. It is interesting that the rules do not provide any bar to a different Judge undertaking the Assessment even though there is that particular advantage on the part of the trial Judge being able to consider all the circumstances. However, the fact that there is no bar does mean that there is a pragmatic and efficient solution to disposing of the costs in a summary way without having to wait for the availability of the Judge who made the Order. In an ideal world, doubtlessly the Judge making the Order would be the one to undertake the Assessment and this may well be possible in many cases. However it is well worth bearing in mind this decision of Coulson J.
Waiting even more months for payment after having finally won a case is indeed an unpleasant experience.