As far ar Tax goes and for that matter anything involving DVLA they have a long way to go.

In reality you can drive your car around for the entire month with no tax disc. Within the first month DVLA don't do anything anyway, and as long as you pay for the full month (even if you buy the tax on the last day of that month) they won't prosecute (and thats only if you should be unlucky enough to get pulled with no tax)

They are piss poor at what they do