My children are adults but looking back I'd say, yes, definitely for secondary school if the child is intelligent and wants to be there. I wouldn't for primary, the opportunities for music, orchestra, extra curricular activities at our state primary couldn't have been matched by a private school.
I'm a bit bitter though because my son got part academic scholarships at the 2 best local private schools but couldn't attend as 'D'P decided family life wasn't for him and left a couple of months before son was due to start, when it was too late to apply for a bursary for the remaining fees. I couldn't afford it alone as a newly single parent with a new baby at short notice.
Son did okay at an outstanding state school (Riddlesdown) but I feel he would have achieved better grades and benefited from the confidence and contacts gained at the private school.
Having said that, I don't feel private schools should exist, they don't in most European countries, they have much fairer systems. All children should get a good education but while they do exist, you can't blame parents for wanting the best for their children.