It is to hand back $32.5 million (£20m) to settle a federal case in the US.
Consumer groups in the UK are now calling for the firm to do something similar for parents in Britain who have lost out.
Britain's Office of Fair Trading warned in September about the possibility of prosecutions after finding "unfair commercial practices" in "free" children's gaming apps which blurred the distinction between spending virtual currency and real money.
The Federal Trade Commission in the US said Apple would make full refunds for any such in-app purchases made by youngsters while playing on mobile phones and tablets and incurring charges without parents' knowledge or permission.
The commission said it had received tens of thousands of complaints about unauthorised charges.