IMO training as a paralegal as an end itself and to improve financial prospects in middle age is a waste of time. generally salaries are not that high and paralegals with higher salaries tend to have years of experience and skills. This is harsh but true. London is even worse, you will compete with kids who have law degrees from all over. Better paying paralegal positions are with successful or big firms and so attract kids with good law degrees and excellent grades who want to get a foot in.
In my first 2 years, I did high level grunt work, maintained clients ( scheduled appointments, organised meetings, did interviews) and did research (compiled cases, fact checking, law document review) in a specialist/niche international firm, I did not draft/prepare any cases/documents despite very good law degree and excellent grades for a long while. IMO, paralegals should have done some of this, but nobody asked me and I never saw a paralegal asked to do legal research. The situation varies in different places.
Not to discourage OP, but the lack of a law degree, any legal training and age is a major barrier assuming you had the interest and aptitude. it is possible to change careers but pple underestimate resources, difficulty and time requirements. I read somewhere that for degree level you need at least six months to establish good study habits. I'm doing a postgrad degree now and i've seen many older students at my uni drop out in frustration or not perform as well as younger students due to time, commitments and other worries. It would not be worth it for GDL, I would go all the way and get the degree.
Curious about what kind of law interests you. You mention being motivated by a lawyer/judge parent and some personal research you did into property law. I suggest more research into legal roles, a paralegal is very different from being a solicitor, barrister, judge, legal researcher and of course it all depends on the sector, law firm and department you work with criminal law, corporate law or private practice. Why don't you talk to lawyer/judge, who is better placed to see where you can go and earn more as well as where he can help with connections.