How to go about finding a musical theatre agent
A great way to find an agent and one I would highly recommend is to start looking for a fringe piece to perform in with the intention of inviting agents to come and watch.
(Which you can find on the CCP opportunities page)
Or alternatively choose a piece that shows your strengths and get together with your actor friends and put it on yourself. There are producers out there also looking to do low paid work and make a name for themselves.
The best location I believe is Central London as most agents have offices there, which means they can come out on their lunch break to see the show: so maybe plan to perform a matinee during the week and an evening show also.
Write the agent a letter, follow with an e mail a few days later then call them a week later and show you are willing and committed.
Most of the actors in the play/Musical/showcase will also be looking for representation, so often it's an idea to club together and send one invite, cutting the cost of postage etc (Also stopping an agent getting 20 letters to the same piece)
And any actors with an agent will invite them along so you have a chance to be seen that way.
Another idea is to keep an ear out for open call's, find out exactly what material you need and if the casting breakdown suits you, and then prepare for a long day but there is a chance you could be seen and offered a re-call or maybe you are right for something else they are casting.
I think one other option is to take a risk, if you know someone who has an agent- check out their website and see if there is a gap for someone like you. If there is then there's no harm in bringing this to light with the agent, you could offer yourself on a 6 month trial, or maybe go and perform some pieces for them or take them to lunch and show your passion. Although this can sometimes be risky, if you act professional and keep it to business this could definitely be a route towards representation for you.