This is terrible. Sadly you have to push and be your own advocate.
The Migraine Trust has guidance on hrt and migraine. It's all online.
Print it off and take it to your GP.
In a nutshell, you can use hrt,
I've had migraine since I was about 11. I've also been on hrt for a long time (with a brilliant consultant gynaecologist, privately, but I was seeing them anyway before starting hrt.)
The consultant youve seen is talking nonsense. No need to any investigations before a Mirena coil as part of hrt.
You don't need a Mirena coil!
I don't understand why the dr said that.
The only guidance about type of hrt with migraine is it's best to be transdermal estrogen - so gel, patches or spray. and most women now use micronised progesterone as the progesterone part.
You've got 2 options- see another GP and challenge them. They don't HAVE to do what the nhs dr told them. (They both might like to do a course on HRT!!!)
Or you're going to have to pay to see someone privately. There are loads of options there, either gynaecologists at your local private hospitals, private GPs or private consultants who offer video consultations.
You shouldn't have to do this privately- it's a disgrace your GP is so ignorant- but it depends how much of a battle you want.