As a mixed-race black mum raising her mixed kids in London, I totally agree that your concerns are legitimate @ReachingOut8. But, could you consider moving within the city instead? As I'm sure you know, one postcode differs massively from the next here. Even a move just a few stops from where you are could make the difference to how safe you feel, as could getting them into the right schools and extra-curriculars. For the sake of your teen especially, I'd look into that first, before considering a bigger move.
I'm best friends with someone who grew up on the Kentish coast and whenever I start fantasising about a life by the sea, she starts up about how she'd NEVER want to move her kids back there, not without literally being RICH. Like PP have said, those coastal towns have some major issues with drug use particularly, and the lack of diversity could cause a serious issue for your DC. My friend dabbled in drugs quite heavily as a teen, for no real reason other than their easy availability and sheer boredom.
Also, as one who lived in a monoculture, don't dismiss the value for your kids of being surrounded by lots of different kinds of people, including lots who look like them. It matters, and unless you live in bang smack in the midst of a very rough estate where your teen is likely to be sucked into badness, the threat of social isolation/alienation could actually pose more of a threat to their (mental) wellbeing long term.
Unless you have significant resources to privately school, and insulate yourself from the deprivation coastal communities suffer from, you'd genuinely be better off taking your chances in (a different bit) of London imo.