Is an out building classed as an appliance? "The load current in any part of the circuit should be unlikely to exceed for long periods the current-carrying capacity of the cable (Regulation
433.1.5 refers). This can generally be achieved by:
(i) locating socket-outlets to provide reasonable sharing of the load around the ring
(ii) not supplying immersion heaters, comprehensive electric space heating or loads of a similar profile from the ring circuit
(iii) connecting cookers, ovens and hobs with a rated power exceeding 2 kW on their own dedicated radial circuit
(iv) taking account of the total floor area being served. (Historically, limit of 100 m² has been adopted.)"
If classing the outbuilding as an appliance then max is 2 kW (ii), unless the connection is near centre of the ring final (i), there are many considerations, one is if warm enough for the freezer planning on being used, I have not worked out fully why some freezers need it to be warm, I can see how a frost free needs to be warm enough not to freezer the defrost outlet, but also seen chest freezers with limits as to how cold room can be.
The second is the load with washer and dryer, the whole point in having a separate washer and dryer is so they can be run at the same time, I will admit I do carefully watch the load with washer and dryer as want them to be solar powered, so washer goes on, wait for water heating to complete, then the dryer goes on. So always within what the solar and battery can provide, often set a delay timer so they don't run together. However when doing that may as well have a washer/dryer so don't need to use a delay timer. Or inspect to see when one can switch the other on. However the 600 watt load from the dryer even with the 2.4 kW load from washer are still just within the 3 kW limit.
Washing machines and tumble dryers seem to have peaked at what they use, I remember the twin tub, and the Bendix which had to be bolted to the floor, both often had the option of hot fill, so the power requirement was low, and with the twin tub nothing else could really be done on washing day, it was dragged into centre of kitchen, and no room to do any cooking. But the front loader started to have weights instead of bolting it down, and we for some reason lost the hot/cold fill, so the power used went up. Again the vented dryer often had the option of one or two elements, so user could select 1.2 kW or 2.4 kW and drying time of 90 minutes or 160 minutes and I know we used the lower setting, but when the condenser dryer came in, often that option was lost, and with the heat pump condenser dryer one only has the one setting, even if only 650 watt.
One tends to look at ones own house, and forget other will not do the same, since for me to go into back garden means going down a set of steps and then whole garden at a slope, no way do I want to carry clothes outside to wash them. Or for that matter dry them, front garden no better. But first house the car port was ideal for drying clothes, it got the wind, but no rain. I also had what wife called the flag pole, with a line which could be pulled up the pole. Worked well, but after all the negative comments was not doing that again.
I did use the garage in mothers house as a utility room, however it was not well sealed, so spiders etc, resulted in not really wanting washing in there.