Obviously, with a first appointment at 11+6, I didn’t have any tests done before 10 weeks. When I queried the date of my first appointment with a local midwife, she said it would all be fine, and didn’t mention any blood tests.
The first scan must be done before the foetus measures 14+1, if you want to have the screening tests done. This is because they need to measure the amount of fluid in the nuchal fold, at the back of the neck, and these measurements aren’t accurate enough to give reliable results after the baby reaches the size of a 14+1 foetus. (There might be other measurements they take at this point, too, other than the length, but I’m not sure what they are.)
At my scan, I was told that the baby was 13+2, not the 12+6 I thought (which was impossible, because I hadn’t yet ovulated on the day it would have had to be conceived. Guess baby is a prodigy who can disregard the space-time continuum, or dating scans are not always 100% accurate, or something). I was glad to have been slotted in when I was, as the midwife had my dates several days out from mine, and a week out from how the baby was measuring!
I had blood tests done at the same time as the scan, for screening (I had other blood tests done at 11+6, for anaemia and various other things, at my booking-in appointment, but I didn’t get the impression these were particularly time-sensitive).
The results from my screening blood tests, the measurements taken at the scan, my age, and whatever else they needed, were put into a magical formula to calculate my baby’s risk of Down’s, and of Edwards and Patau syndromes. They posted me the results a few weeks later. Because baby is low-risk for all three, I am not eligible for further tests (amniocentesis/chorionic villus sampling). I think that if baby had been high-risk, they would have got in touch with me sooner.
In summary, you need to have the scan before you reckon you’re 13+1 in my opinion, in case your dates based on LMP are as far out as mine were! Other than that, there aren’t many time pressures right now - get booked in when you can (and I did wait until 6 weeks and everything was fine - I completely understand why you would want to wait until 6 weeks, too), and pester people closer to 12 weeks if the scan date is taking its time to arrive.