Remove all the "stalks" of the fennel, leaving just the bulb. Remove any hard, weathered outer layers then wash the bulb(s) and thinly slice them. Place the fennel slices into a pan with a drizzle of olive oil. Cook gently for 5 minutes to soften.
Meanwhile, trim the feet of the mushrooms, wash them, and cut them into quarters. Add these to the pan. Season with salt and freshly-ground black pepper and cook gently for a further 4 or 5 minutes.
While these are cooking trim any 'silver skin' off the outside of the tenderloin, then cut into bite-sized pieces. Add these to the pan and cook for another 7 minutes. Add the cider vinegar, the mustard, and 4 tablespoons of water. Stir and leave to cook for a few more minutes.