It can take longer than mentioned above. With HIC it took 6 weeks, with admiral it once took a few hours.
Its all down to the insurance company at the end of the day.
In this period it is important as adam said to have some proof of insurance with you, i normally get them to email me a certificate.
If you are pulled over showing no insurance, and cant prove you do have it (remember insurance company office hours for calling them) then your car will be seized and you will be receiving either 6 points or a court appearance.
Then you will have to argue your case from there that you did have insurance.
Its annoying as hell, and with HIC taking 6 weeks once for me it done my head in, so just carry your docs with you.