Is Sherlock Holmes of BBC's Sherlock independently wealthy?

I was curious to hear what others thought. He seems to have come from a wealthy background judging by his tastes in clothing and music, his education and his brother's connections in government, yet at the beginning of the series he doesn't even have the money to pay for a flat on his own, even at a... show more I was curious to hear what others thought. He seems to have come from a wealthy background judging by his tastes in clothing and music, his education and his brother's connections in government, yet at the beginning of the series he doesn't even have the money to pay for a flat on his own, even at a discount. We see that he and Mycroft don't get along, so perhaps he refused to take any money from his family because they had a falling out?
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