Did you recieve a clear photo/s showing, you had not displayed the blue badge?
If you have not payed, politely write back to tell the company firmly you’re not paying and why you think it’s unfair, but only do this if your confident and willing to take them on. At the same time you can appeal to the association the company is a member.
Another useful site:
https://www.parkingcowboys.co.uk/fighting-back/