Here is version of a letter asking for a salivary cortisol test free on the NHS. You can copy paste and adjust this letter to suit your own cicumstances and or preferences.
A lot of my signs and symptoms are also those of hypoadrenia or adrenal insufficiency. (You may lsit them here, if you want).
The Information in the British National Formulary, Patient Information Leaflets and Drugs.com for Levothyroxine says that prescribing Levothyroxine may cause adrenal crisis in those with adrenal insufficiency.Further, there is an association between hypothyhroidism and adrenal insufficiency. Many experts propose treating any adrenal insufficiency prior to Thyroid Replacement Therapy to avoid adrenal crisis.
A long or short synacthen test is not suitable for assessing hypoadrenia or adrenal insufficiency that is not severe enough to be Addisons disease but a salivary cortisol test is excellent at detecting non-Addison's insufficent levels of cortisol.
The Specialist Biochemistry department at University Hospital Southampton carry out salivary cortisol testing as a NHS service. This service will only assess cortisol (not DHEA) but it is a good starting point. This is a NHS service and it is free for NHS patients. I Should be grateful if you would arrange for the Specialist Biochemistry department at University Hospital Southampton to carry out a salivary adrenal test. Please call 02380 798717 for further details.
It may also be useful to carry out a serum DHEA test to further assess the function of my hypothalamic-pituitary-adrenal axis.