I don't know why so many posters are saying 'no wealth gap' Prep school parents pay a huge deposit when their child is accepted at private primary, not all, but most, mine was a full terms fees I didn't get back till they left the school. Then of course theres the fees, theres no bursary system or scholarship at this age, a handful offer help at 7+, most don't (Not officially) I won't cover uniform as at least one can get those second hand, but not all, there's school trips, much more than friends had for their DC at state primary.
Of those privately educated DC heading into senior school, are from families that have paid in some examples, (like mine) over 100 grand in fees , how does that compare with state primary families that have had none of those costs?? This is a HUGE sum of money my family has sacrificed for education.
As parents we tend to see what we want to see, rather than pretend there's no difference.
Openly discuss this with your child, OP, the differences in households wealth, how private schools attract wealthier families , by keeping it open rather than doing the British thing of sticking your head in the sand and pretending everything is fine, you'll be doing a great thing for your DC.
There will be parents who will judge by your primary school, there will be parents who judge by what you do, your income.
Lucky for the kids, they don't have our hang ups, and your child will be totally accepted by the other kids who may or may not be prep school educated, as I mentioned earlier, its more a thing for the child coming from a more 'normal' background where they haven't been exposed to huge variances in peoples houses and cars, etc.
The fact you are aware of all this, I'm positive your DC will be fine and flourish. There's also a lot more state educated children entering private at 11, its so much more normal now and amongst most parents who did educate their kids at private primary, there's a belief that the indie school selects the best from the state, a healthy respect which is reflected by the school itself, certainly that's what I see.