There are also community gardens who usually do workshops which you can go on and if you can, volunteer for them to gain experience and a good reference.
I used to be a professional horticulture trainer, I had been gardening for a decade in my own garden and allotment, I tried to learn as much as I could about my area which was organic gardening and I ended up working for a national charity and teaching across the country.
You definitely need a qualification, go as high as you can in terms of the RHS qualification and learn those latin names, as it will serve you in good stead when an actual professional asks you a question and you can answer with the proper names and the colloquialism. In fact, long before you go on a qualification start learning the names and what different plants like soil, sun, rain wise long before your course. It will really help you when you get the ID parts of the qualification.
Go on a pruning course, a good one run by a professional. Knowing the difference between leaf buds and fruiting buds, and knowing where and when to prune is a huge skill. And in great demand in the winter when not much else is going on.
Learn propagation. Loads of times I worked with people who talked the talk but didn't know how to take a cutting, or how deep to sow seeds, or what compost was what.
And the most important thing in my opinion, is to know your seedlings. Use the spring to ID as many seedlings as you can out and about rather than just weed without paying any attention to what you are taking out. I walked round a new garden a few weeks ago with a gardener who had moved into her new house in the summer, and spotted many plants growing in the weedy patches that she was planning on buying.
Test yourself, get 10 packets of random seeds that you have never grown before, mix them up and sow in a tray and as they germinate and grow, learn to tell them apart from their seed leaves, and then their true leaves and make notes on them to learn about them. Prick them out as they grow, grow them on and learn as much as you can. If you did that over 5 months you'd learn about 50 different plants and you'd have a garden full, and loads to give away which incidentally, is a very good way of getting people to know that you are a local gardener.