Thank you for all the suggestions! Going to formulate a plan.
We can't have a drying rack as we don't have space. Our downstairs is literally two rooms (kitchen and living room) plus a loo under the stairs. No cupboard space whatsoever so nowhere to store a drying rack out of the way. The hoover lives in the hallway but I recently changed it for a cordless Shark so it can fit in the shoe rack now..We could potentially try those racks on the radiators but we've had them before and the kids are really irritating with taking them off the radiators and trailing them around the house or hitting each other with them. We need as little stuff as possible here! Folding ones might be an idea if I can find some that fold right down out of the way.
I dry what I can outside and we have a washer-dryer. I used to get into a huge muddle with the laundry and have a huge backlog literally taking over one corner of the kitchen but I've managed to train myself to put at least one load on each night, hang it out in the morning if dry or, if wet, put the stuff which can be tumbled back in and put a drying cycle on and then hang the stuff which can't be tumbled on the radiators with the heating on for an hour. That also takes the chill off the house for the kids waking up. We don't get mould as we sleep with all the windows open every night even in December. We run hot as a family - the only time the kids mind the cold is getting out of bed in the morning.
After years of being a complete shambles and living in a complete midden, I've finally got a routine that kind of works - dishwasher on and laundry on before bed (regardless of whether full or not), up in the morning at 6am, heating on, hang laundry out or put on to dry, delicates on the radiators, empty dishwasher, sort packed lunches, kids up at 7am, do breakfast, plates in empty dishwasher, clean up after breakfast, wipe table and kitchen surfaces, hoover kitchen floor while kids play, teeth done at kitchen sink, turn heating off, leave for school, get back from school run (I WFH 2-3 days a week), put radiator laundry away. It sounds very inflexible, I know, but we've finally reached a stage of not having wet and dirty laundry everywhere and I don't want to sacrifice that even if my radiator paint job doesn't last as long 😂. The thing I've recognised with the ADHD is that it's a real battle to embed changes in routine - anything that involves planning to do additional steps (like take drying rack from upstairs bedroom, bring downstairs, set up, put stuff on it) just won't get done. You kind of get stuck in routines. So last year I was consistently 5 minutes late with my kids to school (never later, always 5 minutes), just because we got stuck in a routine with timings that didn't quite get us there on time. You'd think that would be easy to solve - just do everything 5 minutes earlier, right - but actually it has taken a lot of effort and "rewiring" my brain to accept a new routine to get us to a point where we're usually 5 minutes early now.