I had to chase for my booking appointment because the midwife at my surgery had left. It should be at around 10 weeks so I'd give your surgery a call to check all is in order. Once I'd had my booking I got a letter with a scan date, I can't remember how long was in between but I was more like 13/14 weeks when I had the dating scan.
I got mine on the Friday at 12 weeks and scan was three days later on the Tuesday. I was chasing like mad to see if they'd received it and knew it was in hand so I wouldn't worry. A bit more notice would have been nice though.
I got my letter at 6 weeks which was a bit of a surprise but I think that might be because I'd already been booked in for an early scan at 7 weeks. My booking in appointment isn't until next week so probably a bit unusual!
When I found out I was pregnant, at around 4weeks, I called the GP office and they gave me the phone number to local MW Community Health Centre. I called them up, and made my booking appointment and first scan appointment at the same time. So I've known my scan date for least 6weeks now.
I had my booking in appointment at just gone 10wks then finally got my scan letter with a date last week (when I nearly 12wks) but my scan date is when I will be 13wk+4 as my NHS trust say they only do them 2 days a week which probably doesn't help.
I was given a phone number at my booking in appointment to ring and arrange my own scan, which worked out well as I could pick times around work & childcare etc... I guess it depends on where you live.