Formatted MBP. Can't install Mavericks I've formatted my Macbook, and attempting to reinstall Mavericks, but I have a problem.

I access my Internet via an access point that requires me to log in via the web interface. When the formatted finished, I opened Safari to log in, but it froze. I was forced to reboot.

Now when I reboot and hold 'CMD + R' it automatically ties to connect to Apple, but of course it won't until I log into the web interface. So it fails.

How can I get around this? I have no other computers, apart from my tablet, I have no access to the router to plug in the LAN (not that it would matter because the MBP has no ethernet port). I have no CD/DVD drive, and the Macbook doesn't have one either.

Any advice
Did you format your whole drive, or just the Data Partition (usually called Macintosh HD)

If you formatted your whole drive, holding down Command+R will take you to Internet Recovery (if your Mac has either had the EFI Firmware Upgrade for Internet Recovery or it's pre-installed on a relatively new Mac), or else do nothing, and flash a ? mark, indicating that there is no bootable partition on any available drives.

Internet Recovery doesn't work on captive-networks, as you've discovered.

I suggest you take your Mac to an Apple Store, use the Free Wi-Fi to connect to Internet Recovery (if possible), and download your OS from there. 

If Internet Recovery is not a possibility, then I suggest you make an appointment with an Apple Genius, and he/she should be able to guide you through the steps necessary to re-install OS X Mavericks.