Thought it may be interesting if I posted the view of a nanny (me), whose current job was obtained without an agency.
The parents had advertised via a local agency, whom I was registered with. That agency however didn't match me to the job. I found out about the job via an internet site and applied directly to the parents. The position suited me and I seemed to meet the parents expectations. Have now been in the job for 16 months.
I do not know why the agency had not matched me to the job, but perhaps it was due to myself not telling the agency that I would consider such a job specifically, or because the parents hadn't told the agency that they would consider a male nanny (with agencies I tend to find that if parents mention to the agency that they will consider a male nanny, I get to hear about the job, regardless of other factors not matching - which isn't a bad thing, as I could be flexible in what I wanted from a job).
Location can make a big difference as in some areas there are few nannies looking for work, so parents need to cast a wider net and thus use agencies located some distance from their home.
Agencies are great when they make the right match between nanny and employer, but it can be hard to get that match right, and thus sometimes like in my case, the agency does not put forward a candidate, thinking that the job doesn't match close enough for the nanny to consider the position, or for the parents to consider the nanny.
I would suggest that you look for a childcarer privately at first, especially if timescale is not urgent. Then if you don't get any joy, cast the net further by using agencies.