Low estrogen is a concern, it’s needed for joints, bone health and an important for sleep quality. Sometimes when estrogen is low, free T is also low, we convert estrogen from free T so consider the source.
SHBG is lowering your free T, therefore as mentioned earlier low estrogen is expected. LH is better than midrange and T is low suggesting primary hypogonadism in the beginning stages, would like to see prolactin tested.
Do you consume iodized salts? Many in UK are iodine deficient, milk (dairy) has some iodine. Do this, check oral body temperatures per thyroid sticky, if body temperatures are spot on this would indicate good fT3 hormone levels and thyroid labs may not be unnecessary.
If body temperatures are slightly low, iodine and selenium could bring your temperatures to normal. If not suggest full thyroid panel, it will be a struggle to get a full thyroid panel in the UK, doctors like to cut corners.
When TRT is needed usually it is for life unless the cause was not looked into thoroughly (high prolactin) or misdiagnosed. Most UK doctors (NHS) will not make the SHBG connection, SHBG is causing problems shrinking your free T.
In any case you require TRT to bring high SHBG down to free up some T, even if prolactin is elevated. You finely need proper diagnosis before you begin TRT and second time around.