I'm afraid I can't see a chart in the ONS's article which splits by sex and gender identity and age, but there was this: "People aged 16 to 24 years had the highest proportions of people who identified as a trans woman (0.15% or 9,000), as a trans man (0.22% or 14,000), and as non-binary (0.26% or 17,000). The proportion who identified with these categories then decreased with each successive age group.
People aged 35 to 44 years (0.36% or 28,000) had the highest proportion who said that their gender identity was different from their sex registered at birth, but did not give a more specific identity, such as trans man or trans woman. A similar proportion of people aged 25 to 34 years (0.35% or 28,000) answered this way."
More than half of those who identified themselves as female and as having a trans gender identity were below the age of 35. Also "People who identified as a trans man had a younger age profile than people who identified as a trans woman. Those aged 16 to 24 years made up 28.54% (14,000) of those who identified as a trans man, compared with 19.31% (9,000) of those who identified as a trans woman."
I was one of those who took part in the Sex in the Census protest Jellyasaurus - got my paper copy and included the letter when I sent it back though sadly no response. The responses to the census show either significant confusion about what the Gender Identity terms mean, or that many of those who claimed a trans gender identity didn't tell the truth about their sex. This is clear in this passage from the ONS article linked: "People who identified as a trans woman and were aged 16 to 24 years were more likely to have answered male (63.20% or 6,000) to the sex question than female (36.80% or 3,000). In the other age groups, people who identified as a trans woman were more likely to have answered female to the sex question than answered male to the sex question.
People who identified as a trans man and were aged 16 to 24 years were more likely to have answered female (63.35% or 9,000) to the sex question than male (36.65% or 5,000). In other age groups, people who identified as a trans man were more likely to have answered male to the sex question than answered female to the sex question." and this is discussed in the Sex Matters commentary.