Reducing to a 4 day working week - how, what, why, who?!

I’ve been working compressed hours (4.5 days in 4) for around 7 years now. It was hard to start with and I started with Mondays off for childcare then moved to Wednesdays when I realised stuff like museums don’t open around here on Mondays. Yes there was a pay cut and yes the first 6 months were hard to get around balancing things. I work in public sector and pay is consistently below average (ca.£25k take home pa) but made it work. Mortgage was paid off around 4 years back. Still not exactly rolling in it but I get to have Wednesdays to do what I want. Like today I’m still in my pyjamas writing this and contemplating another coffee before breakfast. 
I am flexible with my non/working day; if there’s business critical stuff happening I will move it but otherwise it is not an issue aside from occasionally grumpy boss, but he has control issues. 
I have ADD, GAD and PTSD (all the D’s!) along with a minor brain injury and find the mid week day off helps me reset before the next two days of work. 
I would recommend it. 

My sister used to do a 4 days week to look after her kids but has just gone back to full time as she found that she was expected to do 5 days of work in 4 with a 20% reduction in pay. 

I am considering applying for 4 days a week or 9 in 10 but am weary after the above.

again, thanks to everyone for sharing.

I currently do 42.5 hours a week, so to compress that into 4 would mean 10.5 hours for days a week, which would then impact on after work stuff a touch. Ideally i want to work less in total, rather than less days.

I appreciate the subject of pensions being raised. I dont have a massive pot, despite paying in for many years, but am hoping certain things happen before i get there to allow me to be comfortable enough. But certainly worth looking into further.

I dont think i would have an issue with doing 4 days work in 4 days, rather than be expected to do 5 in 4.

Although maybe a good stepping stone would be the 9 in 10 that a few have mentioned. Could be the perfect compromise for now of work vs wages.

Is there a government or similar website that outlines what constitutes to a valid reason for a company to deny this request? As mentioned before, my employers are a bit old school... and such a request might blow their minds!!