About 40k is usually the minimum.
Borrow the minimum, and repay the portion you don't need. Would an unsecured loan be cheaper for you if you're planning to repay quickly? There are legal fees with a BTL mortgage.
I would be looking at buying for a family member, so I was hoping I wouldn't have to pay the banks legal fees (I don't think all banks charge legal fees on investment mortgages) the issue is the loan size, which wouldnt be above 40k