Hi,
Where is the leak in the pipe -at the valve itself?
It's easy enough to cap a pipe yourself, if you feel you are up to do such.. Once water supply is turned off.
You can buy the pipe cap in a hardware store for a few euro... if you need to cut the pipe, then best to purchase a pipe cutter, failing that a hacksaw & sand paper...
Re washing machines using "hot water", I very much doubt it... but you may need hot water to the shed another time, so I would think it's best to cap it & leave it.