University is both a financial and a personal investment. By having an industrial placement, you increase the probability of finding a well-paid job, which is ultimately what you go to university for in the first place. A degree on its own is not as valuable as a degree with an industrial placement. Remember, you go to university to work at an industry anyways. Nonetheless, judging by what you have written, I believe you have picked Nottingham. This does not mean you cannot find an industrial placement while doing the degree at Nottingham; it is just that Birmingham has basically given you the placement already. University is also a personal investment because it allows you to develop as a person and form a vision as to where you want to be in life, and what lifestyle you wish to live.
To summarise, you are not making a fatal mistake. Albeit, picking Birmingham would have been preferable, but you can still find a placement elsewhere. If you feel that Nottingham has better facilities in general, and that it will help you become closer to self-actualising and making you a better person through experiencing the environment and what the university has to offer, then do not be sad.