It is Illegal in all instnaces to drive any motor vehicle without road tax. (unless exempt by the 25 year tax exemption)
The only time you can get away with driving on the public roads without tax is if you are driving to a garage to have your car MoT'd or driving to a garage to have repair work for an MoT to be carried out. (as you can not get tax without a MoT. the car still needs to be insured.
if you buy a new car without tax you need to provide the post office with a Valid MoT, V5c (log Book), Valid insurance Certificate (origional not fax) and Payment.
if the V5c is not in your name, fill out the part for a new registered keeper and the post office will send this off to the DVLA, this is a safe, and quicker way to get the documents to the DVLA. (saving you the price of a first class stamp)
Some insurance companies (like Adrian FLux) will email you the certificate when you change your insurance, saving time, if you print this out it looks like the origional that they send you in the post and good enough for the Post Office. they will not accept a fax. failing this you will have to wait untill your documents arrive.
in some counties (depending on the rules they have set) this is what can happen
if you are caught without road tax they will impound your car, and give you a fine and charge you removal costs of the car, this can be around £150, then about £40 per day holding charge. they will not release it untill you present a valid tax disc.
the DVLA can also fine you up to £1000, and unlimited for repeat offenders.
if you are parked on the road with out tax, the car can be removed by the council. a little while ago if the car was seen or deemed to be left there on the road for more than 48 hours with out tax the car would be crushed, regardless.
if i was you i'd drive the car the minimum distance you need to and park it off of the road, keep all your documents with you including the receipt and hope you dont get caught. if you do get caught own up straight away declaring you have not tax, but you have only just bought the car. show them the documents and hope you have a sympathetic copper infront of you.