1. Many plumbing fittings are still measured in the Imperial system, even if pipes are Metric!
2. The shank of the inlet valve will be threaded 1/2" BSP (British Standard Pipe).
3. Assuming the flexi hose in your second photograph fits the inlet valve shank, then it is also 1/2" BSP.
4. You need:
4a. A 1/2" BSP / 15 mm compression tap connector. (E.g. Screwfix 58294)
4b. A short length of 15 mm pipe to connect to the tap connector's compression end.
4c. An isolation valve for the other end of the short piece of pipe.
4d. An adaptor to fit the flexi hose onto the isolation valve. (E.g. Screwfix 2665R)
4e. You can get a tap connector with a built in isolation valve, but I don't know where at the moment. If you get one of these you will still need the adaptor (4d above), but you won't need the pipe.