Let me tell you, you haven't even been around the first step to the first hurdle.
I think the reality and demands of any writing career is often undersold and underdiscussed to aspiring newbies. Too much is made of the glitz and glamour, the prestige of an award winning film or best selling book. Often, this false-image presents a too-romanticized, too-innocent version of what the reality is like for writers (mainly focusing, in this instance, on screenwriters, but there's a lot here that's cross-transferable).
The BIG truth is this: everything is SLOW. Everything takes time and everything is about your initiative and proactivity. This is not a career for those who are lazy or just expect, for whatever moronic reason, things to come to them. Worse, things to come RIGHT AWAY. Like, everything get's going in one week and people will sign you overnight to some big honking deal at the BBC or Netflix.
No. No no no no. No. Not how it happens. (WARNING, the word MAY will be used many times in the following paragraphs.)
First, you must BUILD RELATIONSHIPS. If you treat people like stepping stones, show no respect or regard, well, why should they care about you or your scripts? Networking is treated as this grand, impossible, delicate thing, but it's really not. It's basically like any other sort of socializing: just be cool and open. Yes, YOU have to go and meet people. Yes, YOU have to actually talk to people before they can read your script and may, MAY, give you a gig.
Asking to have a five minute meeting with someone in development about career advice, as a graduating/graduate student, or even as a fan of their output, is much less daunting then it sounds. You'd be surprised how generous people can be with their time, as well as how useful being a student is: you're still in school, so you can't sell them anything. You're just a wide-eyed kid with big dreams. They can relate, and if they like you, they may even offer you a read of your script. If they like it, they may give you a referral (an endorsement) which makes a certain 'hunt' that much easier (more on that later).
Research who they are beforehand, so that when you introduce yourself, you can point to something they've made and can say you admire. Nobody can resist a compliment, and thus, that may snowball into a chat, a conversation and, possibly, an exchange of numbers and/or emails. Of course, all this is if they respond: you may have to chase up a few times before they reply. Like I said, slow.
It's also important to be reasonable with your expectations: forget Call the Midwife or Doctor Who or Bodyguard. They are way, WAY out of your league, no matter how good your writing is. Shows like those use writers familiar with the system and who have proven themselves to be able to meet deadlines and turn solid material around in small amounts of time. Guiding a newbie is just not viable. However, that's not the only place to go with your work.
Loads of small theatres and festivals offer opportunities and competitions for material, some may even doing full plays. BBC Writersroom and London Playwrights' Blog are great sources for who has an open slot. That's a credit. Radio and narrative-driven podcasts: The audience is smaller than film or TV, but the advantadge is lower costs, allowing more risks to be taken. Yes, you can just pitch straight to a producer on radio, and may get your work on BBC Radio 4, without any 'unsolicited' guff. That's a credit. Or make a cheap little webseries (superior to shorts, in my view, for writers, and less dicey than a microbudget feature). Credit, credit, credit.
Or on actual TV, preschool's a good place to start grafting: efficient, cheap, fun content and writers who can produce that are always in demand. There'll still be waiting and following up and rejections, but there's far less at stake here for them and you. It's a fraction of what you'd get for a drama, but it's a credit builder with established companies. Remember, you're the newbie, the baby: you can't afford to be snobbish. Kids shows are not beneath you or inferior. They are as dramatically valid and challenging as any 'adult' project.
Now, to round this off, what's a word often associated with writers that has not shown up yet? AGENTS. Here's the honest truth:
You don't need an agent to walk up to a producer or development person and pitch your idea.
You don't need an agent to get you work.
A good logline and better manners will do that fine. Your first priority as a writer, aside from learning and pushing your craft, is build yourself a portfolio, not agent hunt. Show you can do the work, show people want to work with you and show that you have the determination and proactivity to be worth entering a business arrangement with. Credits, specs, stuff in development, awards, all of this stuff counts for a lot and can help you stand out in the pile, bolstered further by the referal from an industry producer.
I suppose the takeaway here is that it's hard. Really hard. Really, really hard. And slow. And tedious. And often times annoying. But I also know I'd rather do this than a soul-draining office job (and I have), and I know this is what I find joy and passion in. Pablo, Cull, my past short films and all the stuff yet to come or still cooking: I've fought battles, felt crushing worry and despair, but I held on. It will happen to you, and it's not easy and it's scary. But if you believe in your material, in yourself, if you keep fighting and taking risks, you will get there.
If you're curious for me to expand on the above, I did an entire series about helping students which you can find here.