I think the problems are complex and so are the solutions. But things that would help:
Better, earlier access to mental health services for adults and children (how many parents are missing work caring for children with mental health issues, or managing work while trying to get treatment for a child who is stuck on a CAMHS waiting list?)
Better access to physical health services, easier access to gp services, quicker referrals, quicker treatments.
More preventative treatments and services. Catch issues before they escalate into problems that mean people can't work.
More understanding from employers that people are humans and have challenges and health issues and lives and families and responsibilities outside of work. Employers expect people to be robots at work, and it's unrealistic. (This is a generalisation, I know, but is certainly my experience).
Wages that mean that people don't need to work every hour god sends in order to make ends meet. If people can earn enough from working less hours a week, that means they have time to cook nutritious meals, shop for vegetables, care for family members, engage in hobbies which support physical and mental health and generally manage their lives outside of work. I like the idea of a universal basic income.
This isn't an exhaustive list. Things like green spaces that everyone can access, better education around health, nutrition, and fitness, a wholesale change in the amount of processed food in our diets, a huge improvement in social care both for workers and unpaid carers, and those recieving care, would also help. There are probably other things too. There isn't a single solution, or silver bullet. It's a whole social, political, cultural change that is needed.
All of these things require time, financial investment, but also social commitment, and a change in social values. And a change in government would be a good start.