Right. I've never managed to post about race on MN without it being deleted so I'll keep this as factual and helpful in respect of the question posed as possible.
Unfortunately I'm not particularly well-connected to any of these small towns and villages but my wife was born and brought up in Burnley. She's mixed race, as am I, but we both 'pass' as white. My MiL still lives on the outskirts of Burnley and we are regular visitors.
Burnley itself has serious race issues, as does Blackburn and Nelson. Whilst the direct, hot elements of it have calmed down a lot since the race riots in June 2001 the hidden, latent stuff is still very much there. Brexit was singularly unhelpful, but illustrative, too: there is a large white 'left behind' working- and under-class caucus in Burnley which resents everything that isn't them. It is a BNP, and formerly UKIP, stronghold for a reason.
In my experience - and I am happy for others to share different ones - it's not a generalised race or diversity issue in the traditional whites versus 'others' sense. It is an Islamophobic environment which manifests itself as a wider anti-Pakistani sentiment. There is also a palpable sense of mutuality to it, none of which is helped by the fact that - in Burnley at least - the white and Pakistani communities live in isolationist ghettos right next to each other, with almost nothing in common. A close white friend of mine married a Brit-born Pakistani and both were effectively disowned by their families; they've moved to the heady inclusiveness of Birmingham.
Not everyone will consciously recognise it and fewer still will admit it, but places like Clitheroe, Whalley, and Barrowford are quite clearly 'white flight' places. I can say that with some certainty. I don't know Read and Simonstone or anyone living there, but - with less confidence - I imagine they are the same.
The few (white, middle class) people I know who live in these smaller places, and the many (white, middle class) ones in the larger towns who want to leave, generally don't have an issue with individual non-whites, but they don't want their own streets and neighbourhoods assimilated into creeping Islamification.
I couldn't tell you with any certainty if the anti-Pakistani sentiment also applies to Asians of Indian or Sri Lankan descent. I do know a brown (Indian) Mauritian in the area, married to a white with mixed race kids, who says he has no real problems. And similarly I couldn't tell you if racism is as much of a problem for black or oriental folk. I've seen nothing to suggest it is on anything like the same scale, or any worse than baseline UK race relations.