Hey OP, thanks for this thread. I have switched my phone to a SIM only deal this morning based on some of the advice here - I'm saving £15 a month now, which covers off Netflix and a newspaper subscription, so that was a half-hour well spent!
First, congratulations on your promotion, your mortgage, your debt repayment and your three degrees! All this with three children (at least one of whom has a cracking work ethic - obviously takes after his mum) and a terrible ex. I am in awe of you.
Have you come across the 50:30:20 rule? The idea being that you spend 50% of your budget on essentials, 30 on 'wants' and 20 on saving. Within that, you might, following the advice on here, want to set aside some of the 50% into different budgeting pots for annual/occasional expenditure like MOT, house and car insurance, emergency fund for repairs and maintenance.
'Saving' also includes debt repayment - so crack on and pay off that £800 asap, then you can start saving. Most personal finance writers recommend building an emergency fund in easily accessible cash first (some people like to keep this in premium bonds - accessible, protected and you get a chance to win in the lottery draw each month).
ARe you in the NHS pension scheme? Please say yes! This was a good decision I made at 22, before I was even really thinking about money and my future - you had to opt out rather than opt in. It's portable across a lot of public sector schemes - or it was - and in these uncertain times, having a defined benefit pension is a great source of security.
But you asked about getting more joy in your life. Good question! I am a fan of experiences rather than things and planning ahead. I find stuff happens if you book it. Lockdown is easing and where I am, a lot of theatres are starting to open up again, and a lot of cheap tickets are available, - could this apply to you and your family? Could you visit Leeds Playhouse or Sheffield Crucible? (you said you were in Yorkshire - I appreciate it's a big county!)
You have a car and your petrol expenditure is quite low - could you plan a couple of trips out a month - picnic and hike? Family room in a youth hostel? (I have happy memories of youth hostels in Lake District).
Declutter and sell/donate stuff? Not so much to raise money, but to get you thinking about what's important to you, and seeing all you have. A lot of personal finance writers advise decluttering as a good starting point for managing money. Get the kids involved in doing this (if relevant)- it gets them on board with thinking about money as well - good life skills.
Yes to getting familiar with Martin Lewis and the Money Saving Expert website - you can get weekly emails. I also like Jason Butler on personal finance - he has a blog,podcasts and a very good 20 point money mastery cheat sheet, downloadable for free. Again, it's a good starting point with children too.
A lot of the PF writers talk about 'intentionality' - knowing what every pound is for, whether saving it or spending it. So you don't fritter.
Oh, and yes, you can reduce your Netflix expenditure to £5.99, but this only alllows one device and if you have others in your household who want to watch, not necessarily with you, it's rather limiting (I found this out by being accused of skinflintery when my son and his girlfriend couldn't log in on his laptop). For £3 more a month you get a lot of flexibility - you have to think about value as well as cost.
Good luck, you'll be grand. Get that diary out and start planning nice stuff.