Hi OP,
I'm sorry that you haven't had a positive first experience with hcps.
Unfortunately as others have said, this is an issue which does need to be dealt with and managed by you, with the support of others such as a GP.
There is no indication to prescribe sedatives to you for blood tests, and that's without being pregnant. No GP would prescribe sedatives due to the risk to the baby and also because they're very strong drugs which must be used with care.
I think your first step would be to register and speak to a GP and explore your options for therapy to minimise your fear of this.
Do you think it would help to understand why blood tests are offered in pregnancy?
In the U.K. we take bloods to check your blood group and screen for antibodies in your blood, a full blood count is also done to check your iron levels and platelets, screening for carriers of sickle cell and thalassaemia is also done and then a screen for infectious diseases such as HIV, Hepatits and Syphilis is also done.
These are done early on to make sure that if you need any extra care or treatment for any of these issues, you can be cared for appropriately and early on to minimise risks not only to the baby you're carrying, but also to you. While people will often say you've got to think about the baby, we also want/need to make sure that you are also fit and healthy.
Now, most NHS trusts use blood taking systems such a vaccutainers, which is a single needle and then little bottles are put on and off the needle - so it's be one needle into the vein, then several bottles/tubes filled from that. Each bottle holds a max of 5-6ml.
Your role in this would be to hold your arm still as any movement makes it difficult to take the blood and can cause injury to you or the person taking it.
I think it may help you to consider what exactly about having blood taken frightens you the most. If it's the though of the pain of the needle going in, then using emla cream may help. Also, if it's a pain thing, all you will feel is a sharp pinch, and then it'll be over. It'll take less than a minute and all you'll be left with is a tiny puncture wound which can be covered with some cotton wool/plaster.
It is important for you and baby to have these bloods taken, and ultimately the responsibility of this does fall to you. If you decide not to have them, the midwife will accept that, but she does have a duty of care to you to offer to take them again at some point during the pregnancy, since prepared that she will ask again.
No one will make you do this, but it is advisable, and attempting to overcome this will benefit you in the long run too.
But first things first, get to the GP and get that box ticked, then have your initial appointment with the midwife to get your booking done and if you're not able to have the bloods done there and then, perhaps make an appointment to try again a few days later?