You're not being impatient. You're first scan should be done no later than 14 weeks which could be next week - see here. I'd phone them back and explain that you may already be three months pregnant and so need an earlier appointment as you need your first scan to be done asap. If the receptionist won't help you then ask to speak to the doctor.
That link suggests to me that if you are 13 weeks now and your first scan isn't done for another 3 or 4 weeks, you may never get an accurate dating of your pregnancy and may not be able to have the triple test.