Hi Jane
I have a Boer War medal roll for the cavalry and F Brook/Brooke is not listed. I think I have found him in the 1881, 1891 and 1901 census and in each he is involved in the wool trade, so I do not see how he would have had time to serve.
You could check for his service papers in WO97 at Kew. They are in alphabetical order, so you do not have to know his regiment. These surviving papers are original documents and you will have to visit or employ a researcher.
Ken