The landlord will probably have buildings insurance. They would need it if they have a mortgage for example. With this buildings insurance, the landlord would not claim against the neighbour as with car accidents but on their own insurance who may or may not go after the neighbour/neighbour's insurance in the background. It's the same when for example the upstairs neighbour's bath floods again and ruins your bathroom ceiling - again. It's your buildings insurance not theirs.
If you have to get quotes for neighbour's insurance company anyway, might be worth saying, 'if £x000, as per this lower quote is in my bank account in 1 week I'll drop the insurance claim for my stuff. If not I pull the insurance claim trigger and it's out of my hands.
If you have to get quotes for neighbour's insurance company anyway, might be worth saying, 'if £x000, as per this lower quote is in my bank account in 1 week I'll drop the insurance claim for my stuff. If not I pull the insurance claim trigger and it's out of my hands.