Sherlock gave Mycroft this tie as a joke one year. Mycroft was so touched that Sherlock gave him anything, so he wears it with pride even though Anthea mocks him for it <--- headcanon accepted. Or maybe he just likes umbrellas that much.
really clever Sherlock Holmes outfit! I would make the skirt a bit longer than that, though. While I really like Benedict Cumberbatch's Sherlock, I think the classic look is still the most recognizable :)