Puberty blockers are used in children, to delay puberty in those with premature puberty. So there is some knowledge about their effects. There is also knowledge about the consequence of natural delayed puberty, and delayed puberty due to other conditions. So this is not an utterly unknown area.
Delaying puberty for a period so long as puberty does subsequently occur is not going to have terrible health consequences. The much bigger risk if from the life long hormone therapy needed to feminise or masculinise.
Delaying puberty from 12 to 16 may be a better option than giving feminising or masculinising hormones earlier in childhood. It gives a chance for some second thoughts, it can avoid surgery. Then consent for further therapy can be given by a 16 yr old 'adult'.
The present service does seem to be providing significant psycho-social support such that the vast majority of children referred aren't proceeding to puberty blockers but a few are.
Delaying puberty in a normally developing child for more than just a few months has very serious negative consequences. There are lots of negative effects, but one of the largest is bone density.
Puberty is a two-part process, governed by both the pituitary and the adrenal glands. The adrenal prompts growth of fine armpit, pubic, and leg hairs on children of both sexes, prompts rapid growth of the long bones in the legs and arms, and when that spurt is finished
it signals the growth plates on those bones to close. The accretion of density in those long bones, however, is governed by the pituitary.
GnRH agonists halt the pituitary process. They don't affect the adrenal process at all. That means that if GnRH blockers are in use, the bones grow longer,
but they don't grow stronger. They become brittle and weak. And if the growth plates close while blockers are in use
there is no way to ever achieve normal bone density.
The pituitary is also involved in the maturation of the sexual reproductive system. In females, hips widen, lactation glands mature, the uterus enlarges, and eggs begin reaching maturity and being released. In males, the penis elongates, the testes descend away from the body, and sperm production begins.
The pituitary is also involved in sex-related development. It plays a role in the development of sexual bonding (as opposed to friendship bonding), cognitive development, and many secondary sex characteristics - things that are driven by sex, but aren't actually reproductive in nature. Things like thickening of the vocal chords, facial hair growth, thickening of leg and arm hair in males; accumulation of fat deposits in the hips and buttocks in females. It also is fairly strongly responsible for our brains and bodies developing the ability to experience sexual arousal and orgasm.
Locking a child out of the fruition of their developmental process, because some adults wish they had a different body type, is reckless endangerment of children in the pursuit of a social experiment driven by a small but vocal group of people who cannot accept their own bodies.