When we try to run our Smeg washing machine we get an error message that there is no water supply. However, the pipes are all clear and the water is flowing (and the filters are clean). We were told that the circuit board needed replacing. Is there not just some way I could re-set the machine?

Kevin.

If you are not getting any hot or cold water, then its possible a board could be an issue. I would check the solenoids just to make sure.
You will also want to check what tells the board to "stop" filling. Chances are that what ever this is happens to be satisfied and the board is getting no signal to fill. I would check any sensors/probes for this first.

If the sensors or probes are calling for water, yet your control board will not allow it to fill then that could be your problem.