If Hertz is happy to believe that you're in the UK, I would let them continue to believe that. I don't think you will have any problems, as long as you're happy to use your Finnish credit card to pay in GBP.

Have you tried going direct to Hertz? You don't need to follow the link from BMI, or indeed use the BMI CDP, to get BMI miles. I always go straight to hertz.co.uk, and can't see any reason why you'd have a problem going to hertz.fi.

Try with and without the BMI CDP, with and without logging in to Hertz, and with country as UK/ USA/ Finland. That's 12 permutations so far...