I see exactly what Rosie is saying above, and it really depends on what you can offer and the sort of child you are looking to adopt. In an ideal world, we would all go through our local authorities (LA) find perfect matches straight away, and get the support we need.
I approached my local authority first, and explained I wanted to adopt a child with special needs. I was incredibly pissed put off by the way they got excited and tried to get me to adopt one of the children they were looking to place. I didn't feel they were listening, at all, to what I was saying I could do.
So, the advantage of a local authority is they do have children (and babies) to place, but the disadvantage is, they will be focussing on finding homes for their children - as that is their job!
In the end, I went to a fantastic agency (pm me for details) and although I had to wait slightly longer, my daughter has been home for almost a year and she is awesome. The support I get is fantastic.
If you go through your LA, and adopt a child from next door LA, they still have to pay the 27k interagency fee - and in my experience, the adoption agencies are not out to make huge profits (unlike certain fostering agencies imho!!)