Armstrong. Do you use the "other" tap?
Eyeball the washing machine hose to determine if it is 1/2 or 3/8 inside diameter.
Go to hardware store and buy a tap/faucet with threads for a hose pipe. This is 3/4 yours maybe 1/2 it will be written on it.
Then buy the requisite hose pipe connector and a suitable hose clamp. Buy large and small if not sure.
Take original tap/faucet off the blue plastic pipe. and replace with the new one.
Cut existing widget off the washing machine hose and replace with the hosepipe connector and hose clamp.