You may find that a conversion master’s in psychology is cheaper. In fact, you’ll definitely find that. There are a number of conversions that would probably allow you to graduate debt free, especially if you did it part time.
However, becoming a psychologist is not as easy as just saying “I’m going to be a psychologist.” If it’s the clinical route you’re wanting to go down, you’ll need at least a year’s paid clinical experience, ideally NHS to get anywhere close to having a shot. Likewise, if you want to do educational, you’ll need at least a year’s working with children. Bear in mind that this is a minimum. People can plug away for years at this career path and never get anywhere. It’s a very, very risky path to invest in. You’d find it easier to get into medicine, statistically speaking.
I would urge you to really consider if this is right for you. Plenty of people say they want to be psychologists without any real understanding of what this means. Many people don’t realise they can achieve the goals they want in alternative careers that allow them to qualify much faster and with more of a guarantee of their investment of time and effort paying off.
If you’ve never studied psychology before, you might find yourself in for a bit of a surprise. A lot of people find it’s not what they expected. You need good maths skills, good abstract thinking skills and something approaching tolerance for computer based models. If you’re interested in people, maybe veer toward something that really puts people at the heart of the degree, like mental health nursing (good route to becoming a counsellor) or occupational therapy or speech and language therapy ie something vocational. Those degrees could have you working inside three to four years. Psychology could be up to seven or eight if ever.
Just think very carefully. If you’re risk averse or debt averse, psychology may not be the route for you. I would urge you to pick up a psychology A level this year, see if it’s really for you. Plenty of distance learning options available. The good thing about that option is that it would also prepare you for studying any of those other options as well.