Just had a phone call off the Council reminding me that after midnight tomorrow I can't drive if my DVLA check doesn't come through. I informed them that it would be with them on Tuesday, I also asked that if it didn't come through would they issue me with a temporary badge? The answer was no, because I'd gone over the cut off date of 6 weeks by one day, they won't issue me with a temporary badge end of.
All this because the DVLA were working to rule and they didn't like my signature on my licence so I had to submit another mandate.
I think it's time to get out of this trade.
You could appeal against the refusal to renew on the basis that your DVLA check had not come back and win, including compensation.
You need to make your licensing unit aware of this.