No private scans for me either. Partly I need to save the money. But also while I understand it's reassuring for some, it doesn't really change any outcome, since there's not a lot they can do if you discovered a problem at 8 weeks. I would probably wind myself up more if the scan were inconclusive because of how early it was. It's my first pregnancy so I've no history of anything untoward. I imagine I'd feel differently if I'd had a miscarriage before.
Of course I didn't expect my local NHS to be quite this sluggish in getting the antenatal ball rolling, naive as I am. That brings on a whole new level of why should I pay for a private scan to reassure myself, just because they haven't even sorted booking in yet and I'm entitled to a scan in 2 weeks anyway. If I get to 11 weeks and I haven't heard, I will be marching down to my GP office and having a public, pregnant, hormonal hissy fit. I'm sure that'll speed things up some. I pay my taxes ...grumble, grumble, rant, etc...