How to approach an agent for representation
Your first step should be taking a look at Contacts, or the Actor's Yearbook. You can usually find Contacts in your local library (make sure it's the latest one as like actors, agents come and go too), and if not, you can get it on Amazon for £12.99 or The Actor's Yearbook for £12.99 as well, or order Contacts directly from Spotlight.
You need to be very methodical and careful about who you are going to contact, so take your time and do it right. Check out which agencies are local to you so you don't spend hours writing a perfect letter and then realising the agency is in Edinburgh when you're in London. So I would recommend you scan the list to see which type of agency you want (Co-operative or not), where it is, and any other information that makes them stand out to you.
From there, get your computer out and have a look at their websites. Again, take your time. Almost every agency has a page stating how they would liked to be contacted - either with a letter or an email, and what information they want provided. Follow these rules, or your nicely prepared letter won't get a look-in. Then scan the website for any clients you might know, recognise who might be working at the moment, and check out the news page for what their clients have been doing. If the last thing a client did was a job two years ago, best give it a wide berth.
When writing your letter or email, keep it polite, concise, professional and to the point, trying to make the important things stand out. Make sure your tailor make and individualise your letter to every agency. If you don't they will pick up on this and chances are it will get ignored. Mention why you would like to go with them, if they were recommended to you from one of their clients; anything that might get there attention and establish a connection. Imagine you are a busy agent with loads of these letters to read every day, and try to think what you would then look for. Always include a CV and your Spotlight details, and again check whether they want a photo too - some don't any more, and some are fine with a photo at the top of your CV. Include a showreel if they ask for one, and if you don't have one, get one first, and then write to them.
Choose when you are writing to an agent carefully as well. This may be when you have a new showreel, when you are looking to change agents, or the best time being when you are going to be performing in a show. This can be a prestigious off West End credit, a fringe production, a showcase evening or a showcase or production at drama school. Bear in mind that if you feel your show isn't really that good or worthy then this may not be the best time to write; you don't want people to see you in something you don't have any faith in, as this could scupper your chances in the future. If you have sent an email, or if the show has a long run, I would recommend you send a follow up email or letter if you have had your show well reviewed, but again keep it concise; just a follow up letter, and not a re-application.
Once done, be patient. I received an invite for a meeting months after sending a letter out, but by that time I had already gone with someone else. And of course, be persistent too. In a great show I was in, I sent loads of invites out but no one came! After the show finished, I decided to keep writing to people to keep myself busy and try to keep riding the wave of success from the show. It got to a month after the play had finished and again I thought about stopping, but still carried on. About two months after, an agent replied and asked for a meeting. We met the next week and I signed the day after. She said she was impressed with my persistence and drive. So it does work.