You might need to seek clarification 'cos in my opinion, having looked at the definitions I would suggest a tractor/quad store is still a garage ( a small detached building).
http://www.planningportal.gov.uk/pe...regulations/approvalneeded/exemptions/classvi
Agricultural buildings are primarily for keeping of animals or growing things:
http://www.planningportal.gov.uk/pe...egulations/approvalneeded/exemptions/classiii
Another complication is that some buildings may be exempt from only part of the regulations:
http://www.planningportal.gov.uk/pe...buildingregulations/approvalneeded/exemptions
For clarification on Building regulations just call your local BC. If it's a rural area they'll be upto speed on exemptions etc. If you live in an urban area you might get some "oooh's" and "aaah's", or even an "I'll get back to you on that"
At the end of the day, it might come down to what the building was intended for, rather than what it's used for now.
But PP may be required for a change of use and with that may come BC requirements.
Or naybe a barn is a barn.
But if your land is not currently designated as agricultural land you may need PP to erect an agricultural building 'cos it could be construed as a change of use.
See para 2.1 page 8 of the following:
http://www.communities.gov.uk/documents/planningandbuilding/pdf/143516.pdf
See also para 2.7: PD rights do not exist for agricultural use near to residential or similar buildings.
Finally consult your local planning and BC for final clarification.
It's better to be sure than to have to dismantle your building, wasting your time, money, upsetting neighbours etc.