Is originality important to you? Are you planning to do the work yourself or have a shop perform the work?
If you want the original seats covers, Mini Mania can supply the trim you need. Alternatively you can buy it directly from Newton Commercial in the U.K. You can install this yourself or have a local shop install it. Only your local shop will be able to estimate the cost of installation.
If originality is less important to you, consider having a local shop make and install new covers for you. Take your worst seat to them and ask them how much it would cost for them to make and install new covers on your seat and compare that to their cost to buy and install the parts you'd buy from Mini Mania or Newton (remember to include shipping costs).
Another possibility is to install aftermarket or used seats. I think there are a number of possible (non-Mini) donors out there. I'm sorry I don't remember the specific types to look for. However, a good pair of junk yard seats and universal seat rails (to mount them) will probably cost as much as professionally recovering what comes with your car.
I'm sorry, I realize I've only given you more to think about without estimating the cost.