If they refuse you your results, they will be breaking the law. The 1998 Data Protection Act gives you the legal right to have them. If they should refuse, come back here, and members will tell you what actions you can take.
OK, so what are you likely to see, and what do they mean...
TSH : that's bound to be there! In fact, it's all a lot of doctors test. Thyroid Stimulating Hormone. It's a pituitary hormone that is secreted when the pituitary senses that there is not enough thyroid hormone in the blood. It stimulates the thyroid gland to make more hormone.
There are many draw-backs to that test, which is why it should not be relied on alone. If, for example, you have a problem with your pituitary, it won't produce enough TSH to stimulate the thyroid, so there will be low thyroid hormone as well as low TSH. TSH is highest early in the morning, and decreases throughout the day. It also decreases after eating or drinking anything other than water. Which is why we always say to have the test early in the morning, and fast over-night.
FT4 - thyroid hormone. The thyroid gland produces mainly T4. T4 is a storage hormone that has to be converted into the active hormone - T3 - as needed. It is converted mainly in the liver, but also in other cells around the body. Free T4 - the name of the test - tells us just how much T4 we have available for use by the body. (There is another T4 test : TT4 (total T4) which doesn't give you any useful information because it includes bound T4, which the body can't use.)
FT3 - the active thyroid hormone. Some is produced in the thyroid gland, but most of it comes from conversion of T4. Same principle as the FT4, tells you how much you have available for use by the body. The TT3 test isn't helpful, and should be avoided.
T3 is our fuel. It's needed in every cell in the body to function correctly - and there are millions of cells. Low T3 is what causes symptoms (symptoms are nothing to do with the TSH itself!). Doctors don't want to test it because, they say, it is unreliable. They don't seem to realise that it isn't half as unreliable as the TSH! I think the real reason is that a) it's expensive b) they don't understand it!
You might, possibly, if you're lucky, have an antibody test : TPOab. If this is high, it will tell you if you have Hashimoto's thyroiditis (aka autoimmune thyroiditis). Doctors don't talk about it because... just because. There is also another antibody test - TgAB - but the NHS never does that - once again, I think that's really because of cost.
Apart from that, you could have a lot of standard tests for sodium, potassium, platelets, etc. But, the above are the thyroid tests. Hope that helps!