Tax question

Hi all Im new here so forgive me if this is in the wrong place

We have had to contact the dvla after not getting our log book. We recived a letter stating that it was beng dealt with on the 30th of this month (my tax runs out on the 31st ) and they told us to ring on the 30th and we could buy it online or over the phone

My problem is we won't have the disc for the 31st (would the email reciept be proof I have bought it ) if we still drove around

Or is it best not to drive it

the only reason its not been taxed earlier is i had to send my new keeper sup to the dvla

thanks in advance