You have until the 14th to retax your car, so you won't get fined for failure to relicence.
However, assuming your vehicle has been being used and kept on the road since the disc expired, you have been committing the offence of failure to display, and will continue to do so until your new disc arrives in the post and is displayed in the vehicle (failure to display is just what it says - it doesn't matter if the vehicle is actually licensed, the offence is still committed if the disc isn't clearly displayed in the vehicle).
I believe the fine for that is �30 (but it could have changed). Getting caught used to be very unlikely, but council parking wardens now report unlicensed vehicles to DVLA, so it is possible that you could be reported for that offence, especially if you park in public car parks or in controlled on-street parking bays (they usually stick a notice on the windscreen, so you would know if that had already happened).
Although renewing online is convenient, it would have been better to have done it at the Post Office in this instance, as you could have got the disc immediately.