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If you can convince upstairs to fix it without going through your insurer there's nothing wrong with that, it's just not guaranteed. You'd have to rely on your powers of persuasion, intimidation, or your upstairs neighbours ignorance of the law and willingness to pay AND to do it to a proper standard. If those things are a possibility it's worth a bash.
However I've been in this situation multiple times and the only thing I've found that works consistently is going via your insurer so they can contact your neighbour and take care of the problem. Either your neighbour has insurance in which case the companies will know what to do, or your neighbour doesn't in which case your insurance company can chase them through the courts for remedy. Either way the problem isn't yours anymore, and that's ultimately what you pay for with insurance.
Fwiw when I did this, I didn't have to pay an increased premium. Suspect this might happen to people with no claims discounts, who then make a claim, but I think that's about it.
Sounds like you're doing it backwards. The last time someone flooded our place we said "you flooded our place, pay to fix it". Why would I fuck my own insurance because of someone else?
British fucking "sensitivities" is why insurance companies are so rich.