Did you make it clear how far along you are?
When I got my BFP, I had a private scan because I wasn't sure of my dates. Turned out I was 12 weeks, so I told my GP two days later.
The midwife and the clinic were fully booked, but they squeezed me in because of how far along I was. Only had to wait a few days to see the midwife, and I had a scan about 10 days later.