Many of the current 'problem' rivers have never been dredged to any great degree. What has changed over a longer period of time is the management of the uplands, so that less water is absorbed and run-off is faster leding to a bigger faster peak in the water level downstream, and hence more flooding.
We are also having unprecedented levels of rainfall - we have had the wettest December in many areas since 1910.
December on track to be the mildest on record | Met Office News Blog
If it was simply the transfer of management to the EA as the site claims the York floods of 1982 (for example) wouldn't have happened. Those floods were what lead to the Foss Barrier being built.