Best way to reduce electric use would be erect a gazebo and run the washing line inside. Then don't need to bring in cloths when it rains, and no bird lime.
But my dish washer for example on Eco setting takes 3.5 hours to wash dishes, uses 0.93 kWh, but on standard setting takes just under an hour and uses 1.18 kWh so 0.21 KWh extra at 20 p per kWh that is 4.2 p to get it done faster. As to needing a energy monitor well all that info is in the instructions.
Washing machine is the same, instructions show 0.15 kWh to 1.55 kWh depending on the wash cycle used. Water use the same between 23 litres and 87 litres. No need for any energy monitor.
The tumble drier time and cost is much affected by spin speed of washing machine, and the cloths being dried, I know my wife tends to sort by colour, clearly sorting by type so higher spin speeds can be used and shorter wash cycles would reduce energy used, but would increase the storage space required to sort cloths into colour and type.
The washing machine is considered as a labour saving device, but to use it will minimum electric and water used likely better returning to the old twin tub, I still remember the cloths sorted into piles across the kitchen floor, cleaner cloths went through first and dirty last, and washing day was a whole days work. Traditionally done day after the oven was blacked and steps scrubbed. The house wife's days were full, she likely worked harder in the home then she ever does today at work.
In the main Eco setting means longer time, and lower heat, but we have the option, spend the time sorting cloths, or spend the money, I should expect I am unusual in that in my house I have a washing machine, tumble drier and a washer/drier, the washing machine and tumble drier I can select cycle and spin speed, and set the temperature low on tumble drier and manually swap cloths between the two, likely better for the cloths, and uses less energy, washing machine is faster than tumble drier, so time in drier dictates how long it all takes, and my wife has to spend a fair bit of time sorting and transferring cloths. And it takes up a lot of space, but utility room used for little else.
The washer drier however takes a long time, but it is a set it off and forget until next day job, one load a day as takes so long, hate to see how much water it uses, as on drying cycle cold water used to condense water out of drying air, the heat used to dry is not settable, and in my mind far too hot. However not a problem with cotton overalls, and it means my overalls do not get other cloths dirty, would not have bought two washing machines, but washer/drier inherited when my mother died. And house big enough to have two kitchens, two living rooms etc. House central heating split into two zones, and 4 rooms only ever heated when we have visitors. Rest of house also has 9 programmable TRV heads so rooms only heated when required.
Odd in a way looking at size of house, costs less to run than old house which was open plan, late 70's early 80's open plan was considered good, idea was one gas fire heated whole of house, and to be fair it could, a 4.5 kW gas fire and flue bricks did work, except there was no thermostat on the gas fire, today we want automation, and we simply don't get out of our chairs to adjust room heating. We did fit central heating, mainly to add control.
We may have a central boiler, but today we heat room by room, be it gas, oil, wood, coal, or electric we want automation, yet we seem to still enjoy getting rid of all the automation and have a BBQ outside!
However to reduce energy use costs money, and once at a point where you can't afford it, it is too late. But at one point I lived in a caravan, when Sizewell 'B' was being built, I found 5 amp was enough, I actually got 10 amp in the end, as my water heating was automated and would switch on same time as fan heater and trip supply, very inefficient absorption fridge, 8 amp at 12 volt no thermostat. Used a 230/12 volt transformer to power it. Fan heater rewired to work series/parallel so 1 kW max but around 250 watt normal running powered via a wall thermostat. Cooking mainly microwave, or simple kettle, the kettle special camping one, 750 watt. Under sink water heater element swapped for a 750 watt version, it held 7 litres of hot water.
Washing done at camp laundrette, shower in camp shower block, no phone not even mobile, only way to contact outside world was packet radio or 2 meter voice, and that only after I passed my RAE exam. Closest I had to internet was Clive the amateur radio packet radio system. Lucky son passed his RAE too at 14, so could keep in contract with rest of family.
Oh did have black & white TV. Well before freeview so 5 channels. It put me off caravanning for years.
Much latter son also wanted to live on the cheap, in his case a narrow boat, he was worse than me with a 4 amp supply, however diesel and solid fuel heating, mainly lived in a marina, but really of no fixed abode, at least by then we had mobile phones, on eco setting with hot fill washing machine he could actually run it on a 6 amp supply, but it tripped the 4 amp supply. It had a 2 kW heater, but it did not run for long enough to trip supply.
But what people want is to have all mod cons but not pay for them, that is not really an option.