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my flat mate last weekend had a bonfire right next to my lovely new loganberry bushes,
anyone think the'll live?

Oh no That doesn't look good. Might live but I doubt that anything will come from those top bits. I'd be tempted to cut them back to a green bit and see what happens but I'd be surprised if you got any fruit this year. I'm no expert on such things though, so don't do it until you hear from someone else ;-)

Fingers crossed that they survive.

I don't think the plant will die as I reckon the roots will be OK but I don't hold out a lot of hope for that branch. I too think it may be better to cut it off and let new growth come from the base. I bet you are cross with your flatmate!