Here are some recommended books by the Black History Month website, the whole list can be found here.
Twenty Eight Pounds Ten Shillings: A Windrush Story by Tony Fairweather
The Making of 100 Great Black Britons by Patrick Vernon OBE
The History of the African & Caribbean Communities in Britain by Professor Hakim Adi
Booktrust's Black History Month Children's book list
Waterstones' Black History Month list