Washing machines & dishwashers with push-fit hoses for the kitchen taps used to be fairly common when these machines were typically wheeled out and connected up when needed.
Most of the units on the British market today have a standard 3/4-inch BSP (British Standard Pipe) connector on the back, the same as the one which is normally used to connect the hose to a fixed washer water outlet.
If you can find a hose which goes from a push-fit tap end to a standard 3/4 BSP connector, then you could just replace the supplied hose with that and hook it up when needed. It used to be fairly easey to find these in plumbing and hardware stores, but I haven't seen one for some time. You could probably still find them if you ask around though, or you could just take a standard hose and fit your own tap end on it.
Apart from the fact that permanently plumbed-in machines have become by far the norm in more recent times, another thing which has probably contributed to the demise of this arranagement is the design of the typical modern kitchen-sink mixer faucet. There's simply no way to reliably attach a push-fit end to many of them.
Edited to add:You might find it easier to just fit a dedicated water outlet for the machine and use the standard 3/4 BSP hose as supplied, even if you disconnect when not actually in use.
Fitting an outlet where you already have the pipework accessible isn't that difficult. You can even buy self-cutting taps which almost anybody can install: Just clamp round the copper pipe and then tighten the valve down. Go to
www.screwfix.com and enter 13768 in the search box for an example.
