Thank you for the kind things you have said about my post.
I've calmed down a little now...!
Swedes, in answer to your original problem: it's likely that the situation is not as straightforward as you think.
Your GP's receptionists are possibly instructed to not allow patients to just ask for a referral for a blood test. This may be because there are quite a lot of patients who think it's ok to just demand a blood test for xyz despite it not being indicated. GPs need to assess whether or not the test is indicated (since the cost of that test comes out of their budget for patient care).
I personally don't think it is unreasonable to think your request could be dealt with over the phone - but a receptionist isn't trained to decide whose request is and whose isn't appropriate to deal with over the phone. Consequently, it may be the practice policy that all such requests are routinely given a GP appointment. Actually you are lucky your surgery a) has enough appointments to do this and b) are offering such a comprehensive service, rather than fobbing you off with a phone call to save their time. Your GP might be able to do more than just order a blood test. Your symptoms can come from more than one problem, and it's worth all options being discussed/examination being performed as indicated.
It is not that unusual for a GP surgery to not do their own bloods, and for their patients to have to go to their local hospital for phlebotomy. But it is not a good idea for patients to turn up and ask for any test without someone assessing the need for that test. And if you want me to go into details of why that is I will, though I think my post is long enough for the time being.
Any GP can understand that dragging a young family into the surgery is a hassle, we do sympathise. But you are actually complaining about your GP being thorough!