That does raise an issue which I've often pondered about registration, the "tax disc," etc.
Just about every state in the U.S. seems to have rules which make reasonable allowances for when you buy a car. For example, if you buy from a dealer you'll get temporary dealer tags, or if you buy privately the law specifically allows you to drive with no license plates for a few days (assuming it's a state in which the plates don't stay with the vehicle when it's sold).
In the U.K. though, there are no such concessions on the tax disc. The law says that you must display a valid license if the vehicle is on the road [*]. So if you buy an untaxed car, you're expected to go and take care of all the paperwork before you can even drive it home. That's pretty inconvenient if you've driven 60 miles to look at a car on a Sunday morning and there's simply no way to obtain a tax disc at the time.
In practice, many people do just drive home anyway (yes, I've done it myself!) and hope that in the unlikely event of being stopped by a cop that he'll be the reasonable sort who'll realize the impracticality of the situation. He can just make a note of the vehicle details and check that the tax is paid within a few days, make sure that the DVLA record does indeed show a change of keeper and then take no further action. That's at his discretion though. If you ran into one of the "Jobsworth" types who wants to boost his conviction rate, you could end up looking at a prosecution. I think the law really needs to make some reasonable allowances on things like this.
* The only exception (as far as the average car owner is concerned) to the "must display" rule is that you may drive to a pre-booked vehicle inspection with no tax disc.
