Ex/Semi Industry here too and what Porcupine says is bang on.
Your best bet at the moment is via Mandy.com. Get some decent headshots (anything under £200 is usually a waste of time) and start submitting yourself for student/no paid films and fringe theatre. Try and build up a showreel via no or low paid work and then start approaching agents with your showreel, you can also invite agents and casting directors to good quality fringe shows. You’ll need a well edited showreel and voice reel and you will most likely need to shell out £1000 at least.
Remember you’ll be competing with well trained actors and those with lots of talent and experience for even those low or no pay jobs.
You absolutely shouldn’t do extra work with a view to side stepping into acting. The more you get known as an extra the less likely you are to get paid speaking roles. You should never include extra work on a CV or online profile.
It’s a very good idea to sign up for good acting classes, especially acting for tv classes. Again you may be able to build up your showreel that way.
Of course the better route is often Drama School if you get in. It doesn’t have to be a three year course, you could do a PG or MA. Even if you don’t get an agent immediately following showcase/graduation, you’d be allowed to join Spotlight and submit yourself for jobs.
Again it’s alot of £££ for Spotlight but you will not be taken seriously in the industry without it.
You should also join Casting Networks.
And be aware it’s not a glamorous industry at all no matter how successful you become. The highs soon wear off in my experience and when I was in high school playing amazing roles in am-dram I had more fun than treading the boards professionally or being on camera.
More often than not, I turn down professional opportunities these days and love having a “normal” job and a more stable life.