Has anyone tried to put an HC-SR04 in a tube.

Ultrasonics can be a tough nut to crack sometimes.
I have found you need a nice clean water surface, no froth or muck, as it will not reflect the signal back.
Also, I would tend to avoid placing the unit in a pipe of any sorts as the signal will bounce of the inner walls and you will most likely not get the reflection you are wanting.
That also means keeping the sender unit away from walls. or other structures.
Hey, I thought you people in the UK used imperial measurements, glad to see you speak metric, has there been a change?

How about using an optical sensor targeting a floating disk or object on the water?
Some of the industrial optical sensors I have used are quite good, albeit expensive. They are typically adjustable for sensitivity and range.

Is the water still or is it flowing?
What is the total rise and fall you expect?

You mention you are not wanting much in the way of accuracy, I would say that +/- 5mm is pretty tight for this application.
Consider also not only resolution, but also repeatability.

rockwallaby . . .