Is a cold fill washing machine economical to run?

Yes hot water can be very inefficient in domestic washing machines. Especially in the UK where many houses have hot water stored in a large cylinder in the airing cupboard upstairs. I have a very comprehensive article about the subject which explains everything in detail. If particularly interested the comments contain many other interesting details and arguments but there were so many comments I had to trim a lot down and close them. Here is the article Cold fill verses Hot fill washing machines

In a nutshell the main problem is that by the time the washing machine starts to get fed hot water it is almost full anyway because they don't use much water any more. Hot water drawn into long pipe runs quickly cools down and is wasted. For example in my house if I want hot water (even at the bathroom sink) it takes around 1 minute before the tap supplies anything but cold water. Downstairs at my washing machine it is even worse. Therefore as I have a modern washing machine it is totally inefficient at using hot water.

Having said all that, if the washing machine was sophisticated enough it could deal with this, but it would not be an easy problem to solve and would considerably increase the cost of washing machines. Manufacturers don't currently think it's a problem worth solving.

Some washing machines may be very close to the hot water supply and not really subject to much of a pipe run between washing machine and water supply. Others may have combination boilers which might be set up efficiently and start to supply hot water to the washing machine quite quickly. These washing machines could utilise hot water and it would help to reduce running costs. Basically washing machine manufacturers decided to design for the lowest common denominator and they just got rid of the hot water valves. This means that most people will get a more efficient machine, but some people, especially those with solar heated hot water, will not benefit from their hot water supply.

Some Miele washing machines do have a hot water valve. There may even still be some other brands that have a hot water valve. Most of them if not all of them though only use the hot water valve on the very hot water settings such as boil wash or anything over 60°. Therefore if you are mostly washing on 40° washes, in my opinion and in my experience, hot water valve is next to useless for most people.