According to the Wikipedia Article on being a British Subject
Before 1949, every person born within the dominions and allegiance of the English and later British Crown was, based on common law, an English and later British subject. To be a subject required only that a person be born in any territory under the sovereignty of the Crown.
Therefore during the Victorian period, anyone born in territories that were part of the British Empire would have been a British subject. So they didn't have to be of British descent.
It does include an important exception;
Within the British Empire, the main class of people who were not British subjects were the rulers of native states formally under the protection of the British Crown, and their peoples. Many such smaller states, especially in India, were for most practical purposes administered by agents of the imperial government, but the sovereignty of all rested in their own local rulers and not in the British Crown, and all such persons are considered to have been born outside the sovereignty and allegiance of the Crown, so were (and, where these persons are still alive, still are) known as British Protected Persons