If you are looking around London, Bucks is the obvious choice.
The grammars in Bucks are not super selective. They admit mostly on catchment. They use a county wide exam. So no sitting lots of exams. Although the secondary schools which are not grammars are not "comprehensive" (as alluded to above regarding Gt Marlow School) the best ones do have around 1/3 of high achieving children. They have 6th forms and get very good results.
Many parents here are not hung up on co-ed or not. Quite frankly they want a grammar. All the grammars are outstanding so people turn a blind eye to co-ed. It is top of few people's wish lists. However, SHF at Aylesbury, RLS Buckingham, Chesham GS and SWBS Marlow and Burnham GS are all co-ed. Some of the very highest achieving, and most sought after, grammar school are single sex.
The key is to choose a catchment area with a great secondary that is not grammar. Just in case. So Amersham, Waddesdon, Wendover, Wing, Marlow and a few other areas have great schools. Housing in central Bucks and North Bucks is not so expensive.
Yes, people tutor. However, the numbers going to the grammars is fairly generous so you do not have to be on the top table! There are plenty of decent primary schools too.