UK mummy's - early scans on NHS..

I'm not sure of due date because periods are irregular. I went to see midwife on Monday just gone (1st sep) and she said she will arrange an early dating scan...how soon do they arrange these?!? I'm dying to know how far I am and plus wanna see baby as well. I explained that I took a clearblue test about 2 weeks ago and that said 3+ which would point at me being 5+ weeks pregnant but then again those arnt quite reliable a lot of people say.