Psychology is ok but isn't the best regarded subject, and it's not a pure science. I think people often do it because they find it interesting and it will give them a degree that they can then use to get graduate level jobs. People with science, maths, engineering, medicine, vet, languages etc will generally have an advantage in the job market over someone with psychology.
Also it doesn't qualify you to be a counsellor. Or a psychiatrist (for that you have to train to be a doctor first then specialise). There are clinical psychologists working for NHS and in private practice, which is a career that obviously applies the knowledge, but I think that requires a 3 year undergraduate degree, then a 3 year PhD, and it's also very competitive to get onto those postgraduate courses.
You can become a 'counsellor' with no qualifications (please don't!) but any decent one would train. I've had a couple of friends change career a bit like you and retrain as a counsellor through BCPC and then set up private practice.
A lot of our nannies and babysitters are psychology students (e.g. tens of them, at a well-regarded uni), and most seem to be going into standard graduate jobs, rather than psychology. Marketing seems popular. Social work in a couple of cases though you can actually get a social work degree instead.
The cool sounding specialties such as forensic psychology are even harder to get into and usually require post-graduate training after a psychology degree. I think one of the London unis has a Masters course.
Could you do something that combines your financial experience and psychology? Whether that's supporting people in taking control of their finances, or working more strategically somewhere where finance and psychology meet?
As a start, to find out if you'd enjoy it, and also to show you're interested should you want to go on and apply for a uni course, have a look at Future Learn, which is the Open University's on-line MOOC site. They have all sorts of free courses inc. psychology-related often. I've done a few FL courses for my own professional development in a different field, and they're pretty good and maybe a good way for you to try things at present.
To check out the best universities for psychology look at things like the Times Educational rankings, for specific subjects at specific universities. To get into an actual psych job you would want to go to a high-ranking university that was also well respected for psychology specifically. Of course, with Covid, nothing is as usual. Most courses are still delivering tuition in person, but are likely to switch online. And some unis are handling the chaos and switch better than others.
(I'm not a psychologist but I know a few, beyond my student nannies, and I also mentor students via a charity and have had a psychology student in the past.)