I personally don't think it's an unreasonable thing to say. Hammersmith is unsafe compared to Hampton. Richmond upon Thames is one of the safest boroughs. Looking at the Met Police Crime Stats with their latest figures. There were 290 crimes reported in Hammersmith and 152 of those at Hammersmith Station in December 2024 versus 34 crimes in the whole of Hampton during the same period. A quick google search shows Hammersmith is 6th in London for the highest crime rates. A quick AI round up shows:
Westminster, Camden, and Kensington & Chelsea have the highest crime rates in London.
Westminster
The most dangerous area in London
Home to many popular attractions, including Buckingham Palace and the Houses of Parliament
Has a high crime rate due to tourist traffic
Has a large police presence and CCTV coverage
Camden
A major tourist attraction with many markets, music venues, and the British Museum
Has a high crime rate, including theft, burglaries, and violent crimes
Kensington & Chelsea
An affluent area that's attractive to criminals
Has a high crime rate, including burglary and theft
Other boroughs with high crime rates
Hammersmith & Fulham: A small but densely populated borough with high rates of violent crimes, theft, and burglaries
Hackney: A popular area with tourists, but has a relatively high crime rate, including violence
Southwark: Has had high crime rates in the past
Of course you have to be unlucky to be a victim of crime but hanging around Hammersmith is undoubtably going to raise the chances you will be a victim of crime. I don't think the fact there are lots of private schools and good state schools in the area has anything to do with the crime rates.