If you have lost the keys & proper lost them and you're sure that they are not going too find them again once you get your new keys from BMW (which are quite quick 1 - 2 days) you can have any missing keys removed from the system (your MINI), so that should anyone find the lost keys the remote won't open your MINI and the chip in the key won't start the car or turn off the alarm if fitted with one (OEM alarm), but it wont stop them being able too open the MINI manually and remove the steering lock

. This can & should be done when your having your new keys programmed but you will need to give them all the keys that you have (this could make the key almost useless if it / they turn up again

).
Too reprogramme used remotes too another MINI you need too have the bar codes supplied with the key when new or I don't think that you can do anything with a used remote (I could be wrong

& I'm not too sure how many remotes can be programmed too a MINI).
On the chip front which are in all keys whether remote or not & needed too start the MINI, the MINIs are programmed for 10 keys hence when you order replacements they will have numbers on the package / bag and the Main Dealers know how many keys are about for that car (not sure what happens if you are clumsy & loose them all the time more than 10

).
If you get new keys always keep the white tag supplied with a new key in a safe place as the tag has all the codes on it for the remote if it has a remote, chip & blade codes (sometimes needed for programming

).
There are key people about now who can do the keys for the MINIs (they will be few & far between) but your best of sticking too BMW IMO as they are not too dear as has been said approx £80 but I think you also have to pay a bit for the programming or approx £20 without a remote as "..Blackadder.." has stated which isn't bad really and that can't really be done much cheaper IMO.