how do I switch on the water supply to my dishwasher?
That is a standard type of valve used in the UK for connecting a water supply to appliances like dishwashers. It is sometimes called an "appliance valve".



Usually the appliance is supplied with a cold-fill water hose that looks like this



Though they vary and sometimes the other end of the hose is permanently attached inside the appliance. 

The blue lever will turn through 90 degrees in one direction only. In your case it isn't clear from the picture whether there is enough room - the wooden partition or the flexible hose "nut" may interfere.

You can actually open the valve by forcing the lever the wrong way. It will break part of the lever but this isn't catastrophic - the valve will still work.

In the worst case you can undo the screw and remove the blue plastic lever. This will expose a  square metal end that you can turn using an appropriate tool (ideally the right sized spanner or socket but mole-grips will work).

If you remove the plastic lever it should be obvious which way it should turn - there will be a protusion in the metal casting that blocks the movement of the plastic lever in one direction.