The main instance of racism in the novel is the students' attitude towards the black teacher at the start. They are rebellious not just because he is a new teacher, but also because he is black. Their behavior includes talking back, not following instructions, and generally trying to make his job difficult. This is a clear sign of racism as they are basing their actions on his race rather than his teaching ability. Moreover, the teacher has to face the silent disapproval or doubt from some in the school community, which is also an instance of racism that pervades the story.
In 'To Sir, with Love', the students' initial lack of respect for the teacher is a significant instance of racism. They come from a background where black people are not typically seen in positions of power or authority, especially in an educational setting. So, they try to undermine him. Additionally, there are likely undercurrents of racism in the way the school community as a whole views the teacher's role. The fact that he has to work extra hard to gain acceptance compared to a white teacher in a similar position points to the presence of racism in the novel.
One main instance is the students' initial reaction to the black teacher. They are unruly and disrespectful, which is partly due to their racial prejudice. Another instance could be the way some of the school staff might look at the teacher differently because of his race. For example, they may not expect him to be as capable as a white teacher. Also, the general atmosphere in the school where the teacher has to constantly battle against the unspoken racial biases of the students and some of the staff is a form of racism presented in the novel.