Andrew, I can't offer work, but I was in the same boat as you late last year, here's what I did.
I went to NICEIC web-site (was not aware of Elecsa or NAPIT or any other 'scheme' at the time), I went to the 'Find an electrician' section and searched on my postcode. The listings returned are pretty much nearest first, but you can go through page after page after page and probably get all the electricians registered with them in the country! I selected only 'Approved contractors' and copied their names and addresses into a spreadsheet (Excel or Open Office (free)) and then did a mail merge and sent a letter to about 140 companies. Using mail merge the letter looks like you've written to them personally and, I think, helped me get a response. I included an SAE with each letter, which I think also helped - people feel obliged to reply if you've gone to a lot of effort, and if they reply they have to think and if they have to think they may remember you when that job comes up next week! Anyway, out of 140ish letters sent I got about twenty replies (not a lot I know), but there were a handful of positive offers, and I've been with the same company since November gaining experience.
If you're not as geeky as me, and don't have the computer skills find someone who is and, if you can't get them to do you a favour then use beer tokens to persuade them. Also, the letter is critically important, before my career change I was, among many other things, responsible for hiring and firing for my previous employer. I saw many hundreds of application letters, and, unless you are 100% certain of your grammar, your spelling (their/there/they're etc), and your delivery, get some help. Ask friends and family to read what you want to send off, get opinions what is good or bad, and suggestions on how better to get across what you want to say - don't waffle (like I'm doing here), edit and get them to read it again, repeat until it's perfect. The letter is the part you should spend the most time on, it's the most important part, it's the only part of the whole project that a prospective employer will see so it's your only chance of persuading them that they should give you a chance.
I hope this helps.