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Mental health appointments for psychiatry are hammered at the moment, sorry.

you would be wise to phone a few providers in Bris and Syd and see if they will accept a referral from an NHS doc, it is unlikely but see what they say. search ADHD psychiatrist.

You have reciprocal medicare so you would need to explain this to them on the phone as the cost for any psychiatrist is around $650-750AUD, the only a exception is if you can find a Doc who can write an authority script based on a referral from your UK Doc. but it's more likely you'll see a GP, call a provider, send your referral and NHS psychiatrist letter and then wait for a date.

complicated huh, you're gonna need to pic up the phone and ask questions so you can prep.