The cervical screening programme now has a 14 day end to end turnaround time target. You should receive your result in writing on or before 14 days (not just working days) from the date of your test.
Many areas of England are now achieving this. I would definitely give your practice a ring if you're after the 2 weeks.
MissAnglia: the cells removed from your cervix are washed into preservative and the vial is sent to the lab.
The liquid is filtered through a membrane, placed onto a slide, the cells are stained with dyes to make them easier to read, then they are read by scientific staff under a microscope. No growing involved! An offical NHS CSP video which explains more - it's about half way in.