We applied for St Paul's, Godolphin, SHHS, Notting Hill & St Margaret's.
We are coming from state school and I would say started thinking about this very late just before the summer holidays after realising we were in pretty much a good state school black hole. Very bad planning by us.
We predominantly used Atom for the 11+ consortium and St Paul's we used the provided materials from the school and bought some similar exams online. We didn't do any tutoring beyond ourselves.
We got offers for Godolphin, SHHS, Notting Hill and St Margaret's. We got through to the interviews for St Paul's but didn't get offered a place.
For the 11+ consortium I would personally say Atom is enough, as the test is pretty much identical to their system. When we started DD would just do the topics as suggested but in the month leading up to the exam, we would just do a mock exams every day. Not saying this method would work for everyone. When we first started we were getting low 100 SAS scores and sometimes lower. By exam time, she was generally scoring 130+ SAS, with Maths & Verbal Reasoning generally 142 most times, with non verbal being easily her weakest subject.
Atom however most definitely isn't appropriate for St Paul's. We only decided to apply for St Paul's in September as a last minute decision. The 1st stage exam is pretty straightforward however the 2nd stage is a completely different ball game. I absolutely can see how tutoring would be beneficial here as math expected here is far beyond the equivalent state level or even 11+ consortium level for that matter.
I think either way, you need a motivated child and either a lot of time you can put in yourself or a tutor if you cannot.