In England you need written material. It may be that if Apple's online system accepts the order and gives you a written confirmation then they are in a contract with you. Their opportunity to refuse is when you place the order.
It's not, in fact. Placement of the order is merely a submission of a request for a product and an offer of payment. The system does not have any capability to reject your order. Computers cannot be granted unilateral agency, and an invoice is not a contract, since it does not require explicit approval by any party. An invoice is used to
generate a bill or a service agreement, which in turn
is a stipulation and would proceed as you describe.
An invoice is a presentation and not a binding document. This is why they tend to say "this is not a bill." It is a list of agreed-upon costs and it is only enforceable for services rendered (not for future services). A sales or service agreement would indeed constitute a contract as you describe, as would any document identifying itself as a contract.
I'm fairly sure this was tested in court only a couple of years ago when the seller tried to argue that because the system was automated they needed another chance - I don't think they got it.
You might be referring to the Kodak case which was big a few years ago. The problem with the Kodak case was that the email included "This contract..." in the terms, the error was not an obvious one (e.g. the price was something like £100 instead of £250, which is not a decimal error or an accidental 0.00 charge), and the error was advertised as a special (not simply tucked into a price list on a configuration page with no fanfare).
Common law provides for the rescinding of a contract made with a "unilateral mistake of fact" and uses a three-pronged test. Essentially the mistake must (1)involve a basic assumption of the contract, (2) constitute unconscionable enforcement, (3) the mistake has a material impact on the seller. A pricing error would be a prime example.