Filling Morecambe Bay with a bath tap

We found this claim at the Leighton Moss RSPB reserve. I have filled a 1.5 litre kettle in 10 seconds tonight using a bath tap. 20 million years is 6.3 x 10^14 seconds. That would mean 9.5 x 10^13 litres of water. There are 1000 litres in 1 cubic metre. This means 20 million years would be 9.5 x 10^10 cubic metres. On  my map, it seems to be 20km across Morecambe Bay from Barrow to Fleetwood. Let's say that Morecambe Bay is a 20km x 20km square which is 400 x 10^6 square metres. Hence in 20 million years, Morecambe Bay would be filled to a depth of 237 metres. That sounds unlikely. Suppose we said 2 metres depth - that would be 200 000 years. Still a long time.