To become qualified you need:
C&G 2365 2 and 3.
C&G 2382-18 18th Edition Wiring Regs.
C&G 2391 Testing and Inspection.
NVQ Level 3.
AM2.
Anything less and you're not 'fully qualified'. The problem is if you cannot get an apprenticeship then you have nothing real to offer except for manual work so personally i would do it the following way:
Do the course, get the qualifications. The course is 17 weeks, two weeks on, two off. Try to get work experience in your two weeks off. Then after getting the certs, you will only be missing the AM2 and NVQ3 which are work-based (NVQ is a portfolio and AM2 is a practical test.) At this point you should apply for work as an electrician's mate, and you will be able to take on basic work like some non-notifiable work. Once working as a mate, complete the NVQ and the AM2 and then you can get your Gold Card, becoming completely qualified. Even once qualified i would advise working alongside another professional as an 'improver' mate, or even working on site in a team, in order to gain valuable experience before heading out on your own if that's what you want to do.
To me, the on-site experience is invaluable since we miss out on a lot of nuance by not working alongside a professional. I understand this route can be the only way in for an adult learner but it's important to not feel like we're seasoned pro's once we have the certificates - you will get exactly the same theoretical training and have to do exactly the same things as an apprenticeship in college, it's just condensed, but the apprentice will be working 4 days a week for 3 years alongside the college which is much more experience which imo can't be replicated.
No offence to the more seasoned vets on here but you really don't understand how hard it can be to get your foot in the door. It can be almost impossible.
Personally OP, you're still a young pup and these courses run all year so i'd have a good old go at getting someone to take you on first as it's the much better option. Be different though. Be personal. Don't just send texts or emails - ring people up, ask if you can go on site for a chat, etc.