It was the same for me 3 years ago. Was seen around 3 months and had the scan short after that
It’s not really about how long you wait, it’s about how far along in pregnancy you are. I think my booking in appointment happened around 10-12 weeks.
When I’d phoned when i was pregnant I didn’t get an appointment until about 8 weeks later, think they tend to base it on when your last period was because it’s easier to date them at roughly 12 weeks