If the spare key is a remote key with good battery it should be fine.
All cars have had to have engine imobilisors fitted for some years now in the UK.
When your other key broke did the immobilizer part fall out?
What year is your Mini? See photos here:
"Here is the key with the circuit board removed. You can see the immobilizer in the back cover; here is how to gently pry it out. It's a sealed unit and you probably won't hurt it but be gentle anyway. Put it in a safe place as well- you DO NOT want to lose this." http://www.mini2.com/forum/first-gen...air-guide.html