The part that RR listed above is a pump but the matching clutch actuator would be separate part and is a multiple of the price.

Have you checked the condition of the clutch actuator on your one (equivalent of standard clutch slave cylinder with an electronic sensor bolted on)? A few years ago I had one of these and the seal that surrounds the rod perished and gradually leaked the hydraulic fluid out and the reservoir ran low (there is a reservoir but it's not at the top on the bay like an M SMG, you have to get to it from underneath).

At the time there were no replacement parts so the whole actuator unit had to be replaced - once it was fixed it had lightning fast gear changes in comparison.

Since then I found that there is now a standard oem slave cylinder repair kit that's around €30 that can be used to fix it. For a standard e46 you'd probably never go this approach as the stnardard e46 manual slave cylinder is cheap as chips. However it makes perfect sense to fix when the electronic version nearly costs a grand.