I’m of the view it’s best to go at the age the schools starts, especially if the majority go then.
So, increasingly schools take their main entry at 11. 13+ Preps are keen to hang onto their yr7-8 and to send the kids at 13. Given they nearly all have to do the exams in yr6 now and then get a deferred offer, the fact they know where they are going, can mean to next 2 years just feels like ‘waiting’ especially if they know people who’ve gone to the senior school at 11.
It is true that if the majority start at 11, starting at 13 is harder socially. Friendship groups have been formed and most of the acclimatisation stuff will be focused in 11+ entry, but 13+ entry getting abit of support, but very much needing to fit in as a minority. It’s harder than most think. The other thing in lots of schools is that you just don’t know how many 13+ entrants there will be. As 11+ becomes more popular, often the 13+ entrants find they are a smaller group than expected. If they’d known that, they might have chosen differently.
It’s different if you’re talking about a school that takes a few at 11 and almost all at 13. However, that’s increasingly rare. And of course, if you’re interested in schools that only start at 13, then that’s the thing to do. If you’re choosing between schools which start at 11 and at 13, unless you’re going for traditional boarding public school, I’d go for 11+ entry. There a reason why most schools and the state system changes at 11. It’s a point where most kids really are ready for the next stage. And one final thing, with 13+ on the decline and quite rapidly, give it another 2 years u til your child is 13 and you could find it’s even smaller and schools are taking fewer still at that point.