I just thought this would be too much for a comment, so I'm prepared to get some downvotes as this might come off a bit negative (not the intention, just to prepare you and I'm a huge pessimist & cynic).
I'm just in my thirties and bordering into Senior level in my field and I feel I can tell a lot about working software (I'm careful with that, senior means a lot of different things and some companies just make you one if you've been working there for a long time). I have worked in small companies and enterprises with xxxxxx employees.
As (Software) jobs are on high demand here (West Europe) it's becoming all more apparent that many people are switching field (to IT) and education does not make a (good) developer, though some form of education to prove you have a certain level of intelligence is highly recommended (many businesses here use it to filter CV's).
Depending on what jobs you're aiming for, higher positions should find your lack of experience slightly easy (assumptions from my part again here), I assume you create some stuff to automate tasks, maybe create some websites/applications for fun, so things that I notice when having interviews or reviewing applicant's code.
- Knowing how to create stuff, but not the why. For higher end positions it is expected you know why the code you write does what it does. And what impact it will have. E.g. would there be impact on memory or CPU. What are the alternatives, and why not use those, language quirks etc. (you need this for bugs).
- No experience in the field. This is very obvious, you'll likely not have experience with Continuous integration, version control (I mean, knowing how to git-commit is not the same thing as working with a team, coding conventions vary everywhere). Handling bureaucracy, people and more.
- Working with legacy; when you learn to code, you're usually starting with something new, how do you handle working in other people's code? Know a sane way to refactor safely?
- Rest assured more questions will be language specific.
Anyways, I just wanted to ramble some items which could be an issue. The problem I foresee might be your age; people of ~40 should be of a high seniority level if you look at development.
This comes with a price tag. It might become a bit of a demotivator if you're making half the income that someone half you age does.
I see that you'd like to working in the gaming industry. Get on the boat, loads of people want this. Fact is, the pay tends to be crap, the deadlines and workload way higher, code quality less important; and to finish it off you're probably working for a gaming platform making mobile/browser games with transactions (At least, that's what's possible here). But keep in mind, as I see you mention C++ and the Unreal engine, that these positions tend to be for the experienced and gifted, not someone rolling into game development in their forties (unless you tend to pull off a great game concept before you start working, since that is how people get those positions at a younger age ;-)). You might want to consider some other technologies. Also I would suggest looking at Unity3D as it is way easier to begin with, though maybe less hardcore development!
However if all those things are fine with you, and you're not in it just to make a lot of money (straight away), you surely can! Just go for whatever position you can get and grow from there, Again culture is a big thing here, but being honest with your interviews and hitting up some recruiters (oh god the UK has many, they even recruit for us) will get you your first job somewhere.
If possible, try to contribute to open source, as larger projects tend to be a little like working in a company and you'll get some proper critique from peers and this is how you grow. Also free track record ;-).
TL;DR; you need experience in this field and yet, that might still not be enough.
However, as markets vary I might be dead-on wrong about what you might need, and hit up some meetups of local companies and ask your future colleagues.