Here is the government guidelines website about this

While there is no official appeals process the guidelines suggest that "You may ask the council to reconsider the case if you think that not all the important information was taken into consideration at the assessment." That could be backed up by evidence that the condition had not improved since the time the badge was granted.

And in practice there can be a formal appeals procedure - for example from one council website: "However Brent Council recognises a person right to complain and as such there is a procedure. Should you require any further assistance in this regard please contact this team."

The basic rule in anything like this is "never take no for an answer". Maybe the National Rheumatoid Arthritis Society could advise.