Yep. The higher the temperature, the more water evaporates from the sea, into air that at higher temperatures can just plain hold more water. The more water evaporates, the denser the atmosphere. The denser the atmosphere, the harder a wind of a given speed will hit and the more energy a storm can hold. And of course the more water in the atmosphere, the more it rains and/or snows.
Water vapour is also a greenhouse gas, so there'll come a point where the warming becomes self-sustaining.
As for whether or not a given downpour causes flooding, that's down to landscape management on the uplands and river control measures as much as anything. More trees and hedges on the uplands (subsidies are currently being paid to rip 'em out, which needs to change pronto) makes the upland soil better able to absorb rainfall before runoff starts and more 'naturalistic' river control to rob storm surges of energy. Cuts have been in the wrong places on this one.
And I'll stop there before the building pressure of the political rant goes into the red...