I assume you mean a classic Mini rather than the modern toss?
Your best bet is to join an owners club (if you have not already done so), get a valuation via them, and insure via a broker that will accept the valuation 0 like Footman James, Adrian Flux, etc.
Otherwise, you are going to get a market value policy, so you'll be lucky to get �500 in the event of your car being written off.
However, be aware that the club valuers may not agree with your valuation, and if you are insistent on tryiong to insure your car for, say �10000, when it may only be valued at �1000 by the club, then you may be a bit disappointed!