Is there any chance your DC would qualify for a scholarship, ie academic, sport, music etc? If so, speak to any possible schools and particular the bursars. DD wanted a difference music experience and new challenge, so wanted to board for Sixth form (previously at state). There were two schools she wanted to apply to and she was offered to two scholarships. Offers varied in terms of bursaries though, first option 45% scholarship, no bursary, second school 10% scholarship, 90% bursary, school uniform paid for. Her first choice had been the second, but going with the first choice every single penny of savings would have gone, and we'd have struggled to pay the basic bills even cutting back.
She wanted to go, found it tough to start with, but recently said it was the best thing she ever did. There are a lot of children from wealthy families, but the other children had no problem with her background. We had children to stay, taking them out and eating on Tescos vouchers, she'd go and stay with others and have £200 concert tickets bought for her, manicures, offers of more than one trip abroad, which we did refuse.
She's at uni now, but still in touch with many and has seen a couple in last month.