Under no circumstances can you drive a vehicle without tax, this also includes when you purchase a vehicle from a dealership. The dealership may tax the vehicle for you before you collect the vehicle, but it is worth asking to ensure that this has been done for you.
If you have purchased a vehicle second hand from a private individual, you will need to sort the tax yourself. To do so, you will need the vehicles logbook (V5C) to tax your vehicle online.
If your vehicle is not taxed, it will flag on the DVLA database, and you will receive a warning letter and a fine of £80. If you fail to pay the fine you will be prosecuted with a maximum penalty of £1000 along with the relevant court costs.
By not taxing your vehicle this could also invalidate your car insurance and/or invalidate any warranty plan.