The single best , most altruistic way to find out your blood group is to become a blood donor.
Not entirely sure why you need to find out your blood group urgently - If it was for an operation or for a blood tranfusion, well if its that urgent then a blood group can be performed in a very short period of time immediately prior to the transfusion or operation.
It is an extremely rare occasion that someone is transfused O Negative blood to combat blood loss - what more frequently occurs is the transfusion of synthetic colloid fluids whilst blood is being at the very least blood group matched / cross - matched.
If you need it for holiday travel or insurance, or because you do motor racing or a dangerous sport, then going via your GP would be the best bet.... you should be able to get a test performed and the results back in less than 2 weeks, particularly if you offer to pay for it.
If it is for a paternity test, there are far more accurate tests out there than a blood group.
Going by what blood groups your parents are (assuming they actually know) only allows you to approximate what group you might be.. not a very accurate way, and a fairly pointless exercise really.