Sorry, meant to come back earlier. My GP didn't do blood tests as mine was very obvious distinct patches, as opposed to general thinning and was alopecia areata. Mine started with a 2inch patch at the back of my head which my hairdresser noticed. I was referred to a dermatologist (I had to go private though) he was very helpful and prescribed steroid ointment (gel, called Synalar), also put me on his NHS list so I only had to go private for the first visit. I was prescribed wigs on the NHS if I needed them and referred to a wig shop for this. The lady there was very helpful, I did get my NHS wig and although that sounds a bit grim it was actually a pretty decent wig.
Over about 6 months I lost about a third of my head hair in distinct patches, mostly at the back luckily, although there were a few patches on top. I have very dark hair and I was very self conscious and distressed. The lady in the wig shop got me some camouflage cream, called Couvre, which was the same colour as my hair and a bit like shoe polish. You put it on the scalp and then comb or pin hair over it, it made a huge difference to my confidence. It was reasonably waterproof, you could wash it off with shampoo, but no worries about getting caught in a shower of rain. I never actually wore the wig, but have kept it just in case.
Anyway, after about 6 months, some of the hair started growing back as very fine white down, which after a few weeks turned darker. Although I was still losing hair in other patches, the rate of loss slowed down and gradually it all came back again. It took about a year for all the patches to start filling in. I haven't had any further episodes, although I know it could happen. I am convinced mine was down to stress, I had had an extremely stressful incident at work a few weeks before it all began. The dermatologist was inclined to agree.
My first post on MN was about this subject as well. I would definitely go back to your GP and push for a referral to dermatology, also ask for your exact blood test results. It isn't just a cosmetic problem, it is a medical issue and the distress it causes cannot be underestimated. Good luck!