David, it'd be interesting to learn a bit more about your case, as it might inform many other cases. Back in the mid '90s, the Valuation Office levied rates on a lot of premises used for storing historic vehicles privately after the Andrews vs Lumb case. Looking at the current VO rating manual and particularly the comment about the reasons for Lumb losing the case, it looks as though they may have been a bit naughty about their interpretation of the ruling, as they used it to rate premises used wholly or mainly for the storage of private motor vehicles.
The current VO rating manual is ambivalent on the subject. It suggests any building used wholly or mainly to store a private motor vehicle (including vehicles, plural) is a private garage and not rateable, but then interprets lorries, taxis, military armoured vehicles and the like as necessarily commercial and goes on to imply that a collection of cars can't be private. These comments are not supported by justification and I can't find case law on them, so I suspect they're open to argument - possibly in court!
http://www.voa.gov.uk/corporate/Publications/Manuals/RatingManual/RatingManualVolume4/sect2/part2/b-rat-man-vol4-s2-ptb.html