They might spike while gentrification is ongoing, especially in the early stages. My hypothesis for this statement is that more affluent people are: 1. More likely to be robbed (ie: they have items that others want), and 2. More likely to report crimes against them to the police. (ie: They trust the authorities, and they might need police reports to file insurance claims (affluent people are more likely to insure their property))
This does not solely reflect lower socioeconomic standing as Pakistani + Bangladeshi communities have higher levels of poverty, and similarly poor areas of cities in Wales and Scotland do not have the same proportionate level of gun crime that occurs in London.