Hi, my DD was diagnosed this year, at age 10, with ADHD (and autistics traits). I think the process does seem to vary a lot depending on which part of the country you are in.
The way it worked for us was that school first suggested we have her assessed last autumn (even though we had considered it for a while). We went to the GP and got a referral to the community paediatrician at a family and child centre. We had the option of that or CAHMS, but where we live CAHMS is completely underfunded and has long waiting lists, and the school (and the GP) told us to go through the paed.
We had two meetings where DD came with us. She didn't really know why, we tried to explain but not very successfully, and didn't mention ADHD. She didn't really want to go and didn't really co-operate, but I think her being there gave the paed a good idea of what she can be like, if that makes sense!
After the first meeting questionnaires were sent out to school and us. These were questionnaires for ADHD, ASD and Aspergers (I think the ADHD one was Vanderbilt, the others slip my mind). Paed also had several long chats with the SENCO at school. School provided very long reports about DD, which we were allowed to read when we went for the next appointment.
At the second appointment the diagnosis was given. There was pretty much complete overlap between our responses to the questionnaires and the schools, and the paed saw her as a 'classic' case.
Since then we have had one shortish meeting and a telephone call with the paed. DD was not at this meeting, and the main topic was medication and behaviour management.
We have since told DD. She was initially was a bit freaked out by it all, but since has been overall positive, and has been flicking through a book we bought called: 'The survival guide for kids with ADD or ADHD'. I don't really know how much she understands, it is impossible to have a coherent conversation with her as her thoughts jump all the time, and, although she talks pretty much all the time, her speech is not great and she often struggles to find words.
We are considering trying medication. She told her younger brother, and his response was: 'what, you mean that she can't help hitting me? oh no, does that mean she will never stop doing it and not even get into trouble?' 
I can completely understand your ambivalence - I felt exactly the same, and I am still feeling a bit confused about it all. But I do think that for DD it will make life easier and better in the longer run, and maybe for us too. I think my own brother probably had similar issues and he suffered throughout school with very little support, and I want her to have an easier time than he did.
For her school at the moment the diagnosis will make no difference, she was already on SA+ and has been getting all the support they would offer a child with ADHD for the past year or so. But it could make a big difference when she moves to secondary school.
We want to have her assessed by an occupational therapist (to assess sensory issues), as this was recommended, but will probably do it privately as the waiting lists are very long here. Apparently it costs about £500.
I hope this helps. Good luck and be kind to yourselves.