The computer system the DVLA now uses gives you something like 3 days grace to get your tax before they whop you with a hefty fine. So as long as you're within that, you'll be OK.
Mellowmama is right, it is illegal, and not having any tax also invalidates your insurance. (hubby works in insurance industry, so i get to learn all the boring stuff!!)
I buy my car tax online or over the phone now, and it doesn't always come on time!!
You won't get fined for not having tax if you have your paperwork with you to go and get tax, but they might give you a 7 day wonder. Having said that, I doubt very much you'll get stopped by police!!
Don't panic too much!!