Unfortunately employment agencies are about as useful as a car with square wheels.
I was in the same predicament a few years ago and yes the job centre are woefully ill equipped to help people with convictions get jobs.
I thought just being upfront and honest was the best policy at first but i learned fairly quickly that as soon as you mention a conviction (especially a sexual offence) irrespective of whether it was a contact based one or not, the person on the other end puts up a barrier immediately, so you might have thought out a genuine and sincere explanation of your offence, full remorse,taking responsibility to get help etc but all they hear is 'blah blah blah blah' and their probably thinking how soon can i move on to the next person.
Lets face it, if you were the employee of the employment agency responsible for recruiting staff, would you want to be known as the one who gives sex offenders a chance ? also pretty much everyone else would be on their side for their decision to refuse you work.
There are many things you can do without having to be employed, being self employed is probably the best way forward since you can't really sack yourself, but the problem there is you may have to re-train and then find business, so it will be slow to start with.
The other thing is writing directly to HR departments of large organisations, especially ones who have a very strong non discrimination policy and who actively pride themselves as being an equal opportunities employer. I personally have not found a job that way, but i did get a few good responses from a couple of large supermarket chains and when i wrote to them i was completely open off the bat about why i was contacting them and the difficulty i had in gaining work.
Personally i work in construction, have had to start right at the bottom and learn a hell of a lot. long hours, back breaking work sometimes, not great pay, but i earn and i have a reason to exist. Construction agencies are lets say, a little bit more accessible for the likes of us and sites are crying out for labour that is reliable and hard working. I know many people i work with who have unspent convictions, some even openly talk about the fact they have just got out of prison, but for my sake i try to keep a low profile.
You need to find work where they don't ask and the work is generally short term. It is going to be extremely difficult for you to forge a long career within a traditional corporate company structure.