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It’s how it’s pronounced in British English.

No it's not. It's pronounced in the same way as the US, unless you're David Attenborough.

Edit: It seems as though others do say slow-th, but it's not something I've really heard from the younger generation

The RP pronunciation (i.e. standard British English) is /sləʊθ/ ... i.e. slow-th, and that's how it's indicated in the OED.