lastnight I have medical anxiety. Refused the blood test at booking in as I was having a panic attack. I'm now being referred to a clinical psychologist to help me so that I will be able to undergo medical tests in the future (it's not just blood tests for me but basically anything medical so at some point in my life this will need to be tackled). I'm actually really pleased at this outcome. It was never suggested during my other pregnancies when they wanted me to have blood tests and I refused.
I'd recommend you ask for a referral too. The stress of worrying about it is bad for you & the baby. Just talking about it with them put my bp at 163/92!
Also you don't necessarily need lots of blood tests. At booking the test is checking for blood type/rh, hiv, syphilis, and if you have signs of anaemia if so they will tell you to take iron supplements. I know my blood type. Don't want std checks. And am taking iron/prenatal tablets anyway prophylacticly.
There is an optional later blood test that is part of the test that indicates if you are high or low risk of Down's syndrome but it's entirely up to you to have that test, not everyone does.
Then I think if you have a normal pregnancy they will want to check for anaemia again later on.
So it's up to you to weigh up the pros and cons of having these tests. You have a right to make an informed choice, although they will try to bully you into following their procedures.