All the times I've been preggo (all 4) I've only ever had a blood test to confirm it once, and that was the first time which was 9 years ago now.
HPT's are so sensitive and accurate now that many doctors don't do blood tests to confirm pregnancy - if you've had a couple of positive HPT's that's good enough for most.

They don't usually run the standard pregnancy bloods (checking blood group, immunities etc) until 6 weeks or later.

I know it seems like a bit of a letdown but it's not unusual. One thing I would be on to though is your referral to the hospital especially if you're going private. Depending on where you live it can be difficult to get in with certain OB's and certain hospitals even if you try to book at 6 weeks. I went private with my last baby and had to book in at six weeks.
Congrats btw!