No, you can't buy batteries from the Apple site anymore, at least not in the UK. Apple have stopped allowing you to buy batteries alone. You're forced to book a Genius Bar appointment, come in and then pay for the laptop to be serviced by Apple at the same time as having them fit the battery for you. (Cost: £129 total).
I spoke to a reseller locally and they said that, anyway, if the model is older than 5 years, Apple classes it as "vintage" and doesn't even manufacture the batteries anymore. So what you're paying £129 for is some spotty 'Genius' to do a system check on your laptop you can do yourself, then fit a non-OEM battery.
The whole thing absolutely stinks. It's a quick way of ripping people off and/or forcing them to buy shoddy Chinese knock-off batteries, and all because Apple claims that people can't be trusted to remove screws and put batteries in by themselves. It's profiteering at its worst and it's exactly the kind of thing Apple used to stand against, not for.
Like the OP, all I want is a genuine Apple battery to put in my (2011, but still working fine) MB Pro. The fact I can't just buy one from Apple is ridiculous.