For the BA.4/BA.5 boosters, the companies have submitted animal data. They have not released those data publicly, although at the June FDA meeting, Pfizer presented preliminary findings in eight mice given BA.4/BA.5 vaccines as their third dose. Compared with the mice that received the original vaccine as a booster, the animals showed an increased response to all Omicron variants tested: BA.1, BA.2, BA.2.12.1, BA.4, and BA.5.

The companies say clinical trials for the BA.4/BA.5 vaccines will begin next month; they need clinical data both for full approval of the vaccines—their recent submissions are only for emergency use authorization—and to help develop future updates. Presumably they will measure recipients’ antibody levels, but not the vaccine’s efficacy against infection or severe disease. Such trials are very expensive and were not done for the BA.1 shot either.
I think the U.K. is using the BA.1 anyway and not the .4 and .5

Weird that I can never remember anyone worrying about this with the updates flu vaccine every year.