How to get seen by casting directors

Firstly I'd recommend going along to some Casting Director Workshops. Companies I use and think are brilliant are The Actor's Guild of Great Britain:
http://www.actorsguild.co.uk/

and Fuse Creative Network:
http://www.fuselondon.co.uk/

Both of these companies host really varied workshops, and attract some big name casting directors (Both have a variety of different kinds of workshops, so worth checking out, and run them in both London and Manchester). I've found in the past that I'm more likely to get a response from a Casting Director if they've seen me before, and this includes if I've done a workshop with them. Obviously, attending a workshop with a Casting Director does not guarantee you work with that person, but it gets your face seen, and it helps to demystify the casting process, which is really useful.

Also, make sure that you're inviting your preferred list of Casting Directors to every production you're involved in. They may not always reply, but chances are they will have read your email/letter, and may notice when you have invited them to multiple past productions. Also, when you invite someone to your show, it's sometimes helpful to divide the invites between your other cast members, and send out a joint email from all the cast (maybe with an e-invite you've made that includes everyone's headshots/spotlight numbers on). When discussing this with your cast, find out if anyone in the cast has personal links with any of the Casting Directors/industry people you would like to be seen by (and vice versa, you can do this for them too). Pooling resources this way is just common sense, and means you all stand a better chance of being seen in the show.

Also, when you send an email to a Casting Director, be really clear about what you're asking them. If you want to be seen for a specific show, then make sure you've done your research and know exactly which part you'd like to be seen for, and why you'd be perfect for that role. They receive so many emails a day, many of them vague, so make yours stand out in a positive way (by this I mean don't try to be "funny", just be professional, knowledgeable and to the point). And be polite. If you invite them to see your show don't make it sound like you're assuming they're coming, tell them they can get in touch with you IF they would like a free ticket (and do always offer a comp ticket, even if you have to pay for it yourself it'll be worthwhile in the long run).

Also, if you have an agent, and you haven't done so already, let them know that you'd like to be seen by a specific Casting Director and your reasons why, and hopefully they'll keep an eye out for you when suitable roles come up.