It seems that there were no specific motorcycle bays, only car and motorhome bays ... which means either that motorcycles can't park there at all, or that motorcycles can park in any bays, as long as they park "considerately". There was nothing on the boards to indicate that the motorhome bays were in some way sacrosanct and not to be used by bikes (or, I assume, cars). Therefore, I don't think the council really has a leg to stand on: their signage is poor but they're just trying to make a bit of money with this "Admin fee", and presumably recover some of their costs in (I reckon fraudulently) issuing the tickets. Typical Town Hall "steal from the motorist" scam.
However, paying the £10 seems the least-painful way to close this matter.
Now if it was cyclists, or drivers of nasty electric cars, that had been shabbily treated like this, the press would be all over them ..........