Sounds like you're having a soggy nightmare! I'd be inclined to have a word with your conveyancing solicitors about this. As it seems to be a regular occurrence when the rain's heavy, the previous owners may have had an obligation to tell you about it (like they do for border disputes with neighbours). If they've falsely said there's never been any flooding of the basement / kitchen, you might have some recourse back to them. Definitely worth a try....
And I hope the rain stops soon!