My DS (now 14) was formally diagnosed with ADD just over a year ago, although the diagnosis really only confirmed what we already knew. We were also dubious about meds (primarily because we didn't want it to fundamentally change him). But the consultant we saw was really patient in talking through all our concerns. When we weighed the pros and cons, we decided to do a trial of medication. It's still quite early days, but it has made a noticable difference to his focus, without otherwise changing him.
I don't have any advice about specific N London schools, but having experienced two secondary schools and now looking for a third (I move regularly with my job), I think it is really worth looking for a school that is the right fit. Being able to look at both state and private obviously opens up your options. And I have concluded that I would always be willing to move / travel to find the right school, rather than settle.
In our experience, a super strict school with a gazillion rules and rigorous enforcement was a disasterous (this was a state comprehensive with otherwise great teaching / extra curriculars etc). My DS is a bright, kind and well-behaved kid, but ended up with loads of detentions for minor "infringements" caused by disorganisation, inattention and general scattiness (forgetting a minor piece of kit, or wearing odd coloured socks). The relentlessness of it was pretty crushing (and the NHS consultant who diagnosed him was dismayed to hear about this treatment, which he said was completely inappropriate for someone with ADHD).
Much more successful has been the more liberal, nurturing and smaller private international school where is is now. It still has high standards and gets the best out of kids (and DS achieves well) but in a more relaxed environment. It also helps that they have a good SEN department, which is properly resourced and provides good support to class teachers (who have smaller classes than the average state school, and therefore more time to implement supportive strategies for those who need it).
We're now looking for a sixth form boarding school in the UK, and will primarily be focusing on somewhere that is relatively relaxed whilst being supportive, that "gets" kids who might have some additional needs (and embraces that) and is absolutely not a hot-house / pressured environment. We're looking at both state and private options.
Sorry, massive essay without specific suggestions. Hope someone will be along soon with those!