Our 2009 Clubman S is missing a plate underneath the engine bay, so we were told, and therefore, somehow, rubbed a hole in the lower radiator hose. I didn't realize this until the low coolant light came on, and by then, I fried the plastic impeller on the water pump. So had to replace the water pump (Got a metal impeller water pump from ESC), the thermostat housing, thermostat, the "plastic pipe" that connects to the thermostat housing, and the lower radiator hose. ~$800 worth of work.. Glad I didn't muck up the head...

 

Your water pump is on the passenger side of the engine. Even though it doesn't seem to be coming from higher up on the engine, this would probably be your most likely culprit. ECS Tuning has a Graf replacement for about $50. That's what I used and I am very happy with it. The water pump makes a "joint" with the water pipe that travels across the back of your engine to connect with your thermostat. So, unfortunately, you won't be able to know which side of the "joint" you have a leak on until you get in there. I don't like to do things twice, so I'd advise just changing the water pipe at the same time. It's made of plastic, and any Gen2 car is old enough for it to have degraded. So now you're looking at another $100 bucks or so. All told, you can probably fix your problem for under $200, and about 4 hours of your time.
Also, if you're running out of coolant and you aren't getting a high temp alarm, you probably have a bad coolant temp sensor as well. My advice here is to just buy the OEM MINI branded one. I tried an aftermarket one from Amazon, and ended up changing that one out, too. (One of those do it twice things. Ugh!)
Straightforward, tedious work that doesn't take a ton of technical skill, just patience. I really think this is your problem, because it sounds EXACTLY like mine.

 

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Hey! Thanks for the reply! I actually just saw this after I took it to Tiresplus so they could lift it and see where the leak was coming from as well as do a compression test.

Turns out the water pump is apparently fine, only issue is that the friction wheel/pulley is making some noise. The leak itself is actually (from what they can see) coming from the water pipe that goes from the pump to the thermostat and from the thermostat housing. So basically you were there!

I can figure out how to change the thermostat housing easy enough, but can't find anything that'll help me change the pipe. Got any how to's for that from when you did it?

Thanks in advance!

Thoughts on replacing the friction wheel/pulley

 

Very, very typical. The reason I mentioned where the pipe "meets" the water pipe is that is usually where the leak is. There's an O-ring between the two that wears out. But, from your description, maybe the water pipe itself has a crack or leak in it? Also, it may not be the pulley making noise, unless a belt is slipping (?), but it could be your water pump that's driving it. Food for thought.

So, if you're doing the work yourself, I would just do all this at one time, and know that everything was good to go for the next 60k miles or so (YMMV):
water pump
water pipe (and o-ring)
thermostat
coolant sensor (bite the bullet, and buy the OEM one)
Also, just look at the friction pulley rubber on the outside of the wheel. If it looks pretty good, you can probably keep using it. A new wheel is only about $50, so if you have any doubts, again... touch it once...

To change the water pump, I took off the upper passenger side motor mount and lowered the engine a little bit with the bottom mount still attached using a floor jack, so that I could get my hands in there. It's tight! The water pump is about 1/2 the price of the water pipe, so I just don't know why you just wouldn't change it while you're in there, whether it's leaking or not. The aftermarket pumps are upgrades from the OEM ones, anyway, IMHO.
Here's the deal. You CAN change the water pipe out without taking the intake manifold off, but I would never fight it. Once you have that off, everything is right there for you to replace. The hardest things about doing this work will be getting the intake manifold off (that bottom 10mm bolt is a PITA), and getting the water pump and pulley in place (it's pretty tight quarters even with the engine "tilted" a little bit). There's nothing too technical about the work, though, it's just tedious, and will probably take you half a day if you've ever turned a wrench before. Also, my dealership wanted $1100 to change just the water pump out - you can do all this for probably $400. Your call.

Feel free to PM me if you want more detailed discussion.