There's a reverse trend that coincides with an increased uptake in younger groups: The age-specific death rate for "10-59 + Second dose" in June was 2,8 and went down to 2,4 in September.
One thing to keep in mind: When we're talking about the 10-59 age group on their second shot prior to April, that's only a population of 800k with a total of 16 deaths reported between January and April. Confidence intervals for this period are very wide and the upper confidence limit in the ONS data is quite close to what they're reporting e.g. for September.
[1]: https://coronavirus.data.gov.uk/details/vaccinations?areaTyp...