As Another76543 said - and also worth every penny in my view. But it depends on choosing well, and not only looking at schools that cater for the whole 3-18 yrs as the original question suggests, because you can't predict what your children will be like at 11 or 13. You would need to decide on whether they will take the CE/scholarship route at 13, or if they will do the 11 plus, because a 3-11 school takes away the choice.
My children went to three different pre-prep/prep schools from 3-13, because the first two in one way or another proved not to be up to scratch, but we reckoned that all of them had multiple advantages over all of the state alternatives (ranked as "outstanding", for what that's worth).
Forget class size although (unlike for secondary education for which there is no evidence) there is some evidence that class size is important at this stage, and forget social cachet and all that sort of nonsense. What you should get is:
Subject-specific teachers with degrees in those subjects from decent universities. The school should list its teachers and their qualifications in its promotional literature and a few MPhil/PhD/DPhils in the right subjects is a good sign. This was the first filter that we applied when shortlisting schools.
Latin and ideally Greek. This is evidence that the school governors/head are prepared to invest in subjects that have great educational value, even though some parents might not regard them as essential.
A long school day. Rather than clocking-off in the middle of the afternoon there should be an 8.30 to 5.30 or 9 to 6 school day with competitive team sports every afternoon on the school's own on-site grass pitches. There should be match reports in their promotional literature to give you an idea of the ethos of the school, matches played against similar independent schools involving some travelling, and there should be no matches against local clubs - because they won't be good enough - if the school is doing it properly.
The extracurricular stuff is a given.
A list of leavers' achievements in scholarship exams and future schools.
The benefits of a good prep school are lifelong, and probably greater than from secondary education, which is much shorter and too late: "Give me a child until he is 7 and I will show you the man."