There is this great article that I read online once, and it really inspired me ever since. A vacation scheme student, who for 4 years after graduating, kept applying for a Training Contract and almost eventually gave up. On his 4th year, he decided that he would quit law if he gets rejected another time. Luckily, after these years of resilience and determination, he was offered a TC at
Hogan Lovells (a great firm, may I add). He had a personal conversation with the partner there, reflecting on his years of applying. When they were sitting together, he told the partner that he had received a ton of rejections previously, and thought at one point that a TC would be impossible for him. The partner smiled, and got a bit shy - he said something that really does formulate the moral of this story - "I received more rejections than you" he said, "but that is why I'm here on this side of the table".
The term in itself, "Rejected", is so harsh and unnecessary. In my view, it is a step closer to success. You're benefitted in so many aways - imagine working at a firm that may not be meant for you? These "rejections" make you familiar with the firms, educates you on your choices, makes you wiser, and tells you on how you can improve (most often, you can request feedback from the firms!) I know things may be tough, and I got rejected from HSF too (stupid WG test), so I've been there, but know that so long as these City firms still give training contracts and vacation schemes, then there will always be a chance for you. It is the determination that is needed to continue in the face of the "rejections", or experiences as I like to call them
Keep me posted on how the rest of your apps go, and best of luck!