tech,
It takes anywhere between 4 - 8 weeks to get the NHS card. For one of my friends, it took 12 weeks! When you registered with the GP, they should have given you a bunch of documents detailing the various doctors/consultants available in that GP, and the name of the consultant you will be seeing, and modalities for getting an appointment with the GP. And if I remember it right, they should have taken an initial blood & urine test before or during the registration. If you have all this, then you don't need to worry about when you will get the NHS card as you are already registered with that particular GP.
You will need the card though, since that will give you the NHS number and will be *really* useful when you move move and shift into a new place.
On the light side, if you are from India, you will find that NHS is a overstretched health-care system similar to our public health care, but private health care in England is very,very expensive even by English scale! The flip side of being in a developed nation
Regards,
Dhilip