If you want to connect up a washing machine that uses hot and cold water (and therefore has a hot & cold fill valve) but you only have a cold water supply available, you can use a Y Piece connector to connect it up to a single cold water tap.
The washing machine will then work OK, but it may take longer to wash than normal. However, it may not be significantly longer and you may also get better wash results if it takes longer to wash. Simply screw the Y-Piece onto the tap, and then screw the hot and cold fill hoses to the Y-piece and connect the other end of the fill hoses to the washing machine. (You may also be able to buy this part from a DIY store like B&Q)
What if you just leave the hot fill hose unconnected?
If you don’t connect a water supply to the hot valve (and simply connect the cold water hose to the cold valve leaving the hot valve with nothing connected to it) then some wash programs may not work because some wash cycles only fill with hot water and will fail or produce an error without a water supply to the hot valve. However, some washing machines may work OK with only the cold fill hose connected. You could always try it and see.
The worse that will happen is the washer could either stick on the odd wash programme or may abort with an error on some. It’s better to use a y-piece if possible so that water is supplied to both valves as designed. The washer will not know the difference between hot and cold water and will just heat up the cold water to the correct temperature.
The washing machine may now use slightly more electricity, but if it’s less than 10 years old it shouldn’t be significant unless you use a lot of 60 or 90 degree washes because they use relatively very little water on wash. On 40 degree washes, manufacturers actually argue it’s more efficient to fill with cold water only and slowly heat up the water to 40 degrees as described in detail in my article here – pros and cons of cold fill washing machines.
If you have a cold fill washing machine and have both hot and cold taps at the plumbing abnd want to know what to do with the unused hot tap check here – what to do with the old hot tap when connecting a cold fill washing machine