My understanding is that you should have a test during early morning like before 10am without having had any food. This will give you the maximum level of TSH. But if you wanted minimum level of TSH, you should take your sample in the afternoon when it's lowest or does it matter?
Also, do you think you can influence the test result depending on which part of the menstral cycle or does it matter at all?
TSH is highest early in the morning - long before 10 am! 8 am would be better for a test if you want a high TSH. It then drops throughout the day, and after eating. For the lowest TSH, best to test late afternoon. I'm afraid I don't know about the menstrual cycle.
Due to doctors not relating any of our clinical symptoms to hypothyroidism they seem to solely only look at a TSH result and maybe T4. Nothing else at all.
If TSH is 'somewhere' in the range - even at the top - many doctors will stop increasing dose. If a TSH is very low they will jump to the conclusion that we have gone hyperthyroid (which is impossible if hypo) and reduce dose with return of symptoms of patients.
Early a.m. we find suits us, the patient, best as TSH is higher then and drops throughout the day.
Procedure is - the earliest blood draw possible, fasting (you ca drink water) and allow a gap of 24 hours between dose of levo and the test and take afterwards.
If you take food before test this also reduces TSH.
Can see from your other posts you have B12 injections?
Are you diagnosed as having PA - as this is autoimmune it would make autoimmune thyroid disease (Hashimoto's) more likely
For full Thyroid evaluation you need TSH, FT4, TT4, FT3 plus TPO and TG thyroid antibodies and also very important to test vitamin D, folate, ferritin and B12
Private tests are available. Thousands on here forced to do this as NHS often refuses to test FT3 or antibodies
thyroiduk.org.uk/tuk/testin...
Medichecks Thyroid plus ultra vitamin or Blue Horizon Thyroid plus eleven are the most popular choice. DIY finger prick test or option to pay extra for private blood draw. Both companies often have money off offers.
All thyroid tests should ideally be done as early as possible in morning and fasting. This gives highest TSH, lowest FT4 and most consistent results. (Patient to patient tip, GP will be unaware)
If antibodies are high this is Hashimoto's, (also known by medics here in UK more commonly as autoimmune thyroid disease).
About 90% of all hypothyroidism in Uk is due to Hashimoto's. Low vitamins are especially common with Hashimoto's. Food intolerances are very common too, especially gluten. So it's important to get TPO and TG thyroid antibodies tested at least once .
Do you supplement any vitamin B complex?
If you are taking vitamin B complex, or any supplements containing biotin, remember to stop these 3-5 days before any blood tests, as biotin can falsely affect test results
Thank you for your helpful advice. 
Yes, I have PA and self inject B12. I didn't know about biotin so will stop taking multi vitamin beforehand.
If you have raised antibodies (Hashimoto's) then you probably need to avoid iodine (in most multivitamins)
drknews.com/iodine-and-hash...
thyroidpharmacist.com/artic...
Usually recommended on here to supplement individual supplements
Eg if tested and levels are low
Vitamin B complex
Vitamin D (plus Magnesium and vitamin K2 Mk7)
Iron plus vitamin C
At the moment, I inject Vit B12 every so often and take about vitamin D (4000IU) everyday. I don't know if I have Hashimoto yet. Need to do the test for that.
Timing of NDT for blood test
Best time to take first NDT blood test 
Best Time of Day for Cortisol Tests
