There is a little known fact about Mycroft Holmes's umbrella. It is the real reason he always carries it on his person. He doesn't trust anyone else to use it appropriately or for the greater good, and thus never lends it out. Actually, while we're here, I might as well mention that he's never used his umbrella as an umbrella at all. He has other umbrellas to use, or he remains inside. The simple black umbrella that Mycroft always has with him is so special; it has its own special resting place at night, away from the other, less special umbrellas. They don't really like that, but what can they do, they're umbrellas.
The real secret behind Mycroft's umbrella is that it enables the user to fly. You can't just open the umbrella and tell it to take you somewhere; there is an art to the flying. One must stand straight, with their heels together and their toes apart. The arm not holding the umbrella must remain by your side while the arm holding the umbrella should be bent at a 15 degree angle at the elbow, which remains at your side.
Mycroft had the umbrella appropriated from a nanny, along with a supposedly bottomless carpet bag and a measuring tape that gave you your name and personality based on your height. The nanny managed to escape with her carpet bag before questioning, but Mycroft retained the umbrella and measuring tape (It told him he was dashingly debonair, if not a bit feminine). When he received the umbrella, it had a disgustingly unusual handle, a brightly painted parrot. Mycroft had that fixed right away and hadn't parted with the umbrella since.
Besides, it was great fun to float away to the look of loathing on Sherlock's face.