Hi
Two things:
The NICE Clinical Knowledge Set is what your GP should know about specific diseases. There is one for Addisons Disease (Adrenal Insufficiency) and you can find it here
https://cks.nice.org.uk/addisons-disease#!scenario. It's worth reading the section called follow up where the issue of emergency injection material is explicitly covered. The item you need prescribing currently is Hydrocortisone Sodium Succinate, 100mg, added to this you will need Water for injection, 2ml - that is 2 separate items on the prescription unless the GP will only give you a single dose. You will also need syringes (at least 2ml 3 or 5 ml better) and needles (green or blue at least 30 mm long unless you are very skinny). For some bizarre reason your GP can't prescribe needles and syringes for this but may be willing to give you a handful alternatively try the practice nurses. You can also buy them from the ADSHG (with a useful box if you like) at
http://www.addisons.org.uk.
The wording on medical bracelets is always a challenge. I asked at the recent SWAST conference day and even the paramedics couldn't agree. My eventual choice for the UK has been: Name, Date of Birth and NHS Number on the front then Addisons Disease, T2DM, Astma and Acromegaly on the reverse. That way they can at least access my Care Summary Record.
For overseas holidays I have a separate, larger bracelet which lets me put all that on the front and its also got a broad red silicone rubber strap to make it obvious. The reason for Addisons rather than adrenal insufficiency or hypopituitarism is simply that the Joint Royal Colleges Ambulance Committee 2017 update (and the earlier 2006 version) explicitly index on Addisons Disease but not on adrenal insufficiency so it's easier for an EMT or paramedic to reference.
All the best
Tim