It's highly unlikely that the DVLA will chase people for a three-day delay - that can be the result of our totally inadequate postal system - and that's the excuse you should use if they do come for you. They are far more likely to put their resources into catching habitual defaulters with months or years of unpaid tax to recover, so I wouldn't panic too much this time.
Agree with Andy (for once!) ;-) You won't be fined I'm sure. If you go the local PO and get it soon I'm fairly sure there is a "window" in which to renew. (No pun intended - or was there!)
I've been out of the country on business and when I returned my car tax was a month overdue. Went to the post office looked shame-faced, apologised repeatedly and got the new disc with no problem. 3 days is not a problem at all.
It always used to be generally understood (rightly or not) that there was a 14-day grace period for renewing tax. I also believe it's not enough to buy the disc. Not displaying an up-to-date one is an offence.
Correst Ewood .... the 14 day period of grace does not exist ... reminders are (allegedly !) sent out giving the owner plenty of time to put tax on the car .... DVLA then argue you have no excuse .... it is both an offence not to have tax and, if you do, to not display it .....
I recently realised my car tax was nearly a month overdue- no particular reason, just stupidity on my part- and rang the DVLA. They just said to go to your local DVLA office before the end of the month and I got my new disc with no problems. I'm assuming that if I'd done it after the end of the month there would've been a fine.