I don't mind paying the original fine
Blue badge holders are not subject to the time limit and the photos show a blue badge on display, but it looks like it expired:



Have you since obtained a new one?
The process is now to wait for the Order for Recovery, and then file a witness statement on the ground that you made representations and did not receive a Notice of Rejection, the process is explained here:
This section explains the enforcement process for a parking Penalty Charge Notice, where the vehicle was not clamped or removed.
Read from the charge certificate paragraph down to the bottom of the page.
You cannot rely on the post, therefore you need to keep an eye on the amount due on the council website. When the OfR is issued the penalty will go up to £129, at that point even if you haven't received anything in the post you can download
form TE9, fill it in on your computer (don't do this yourself, ask us for help and we'll explain how) and email it to tec@justice.gov.uk