The water stops at the connection on the back of the washing machine. When
it wants water it opens the valve.
Assuming it's the correct adapter, it probably does just need tightening.
Alternatively, take the taps off and fit a pair of small appliance valves.
Are the taps feeding anything else?

The taps don't feed anything else, so changing them wouldn't cause any
particular problems (just the cost of getting someone competent to do it).
I'll give it another go tonight and tighten it as much as I can to try
again.

Thanks for the help

Lee