It's usually possible to disable Secure Boot without disabling EFI support; however, the user interfaces in EFIs vary greatly from one system to another, so I can't provide step-by-step instructions for doing this. I recommend you peruse your firmware settings to find the relevant options and play with them.
Also, it was my understanding that 12.04.2 did support Secure Boot. 12.10 definitely does, and I assume that the new 13.04 does. Thus, you should be able to get Ubuntu installed with Secure Boot active. Even if 12.04.2 doesn't actually include Secure Boot support, trying 13.04 might be worthwhile. Admittedly it's not an LTS version, but given how new Secure Boot is and how quickly things are changing in this arena, giving up LTS may be the price you have to pay -- at least, to do it relatively easily.
If all else fails, you should be able to get it to work by creating your own Secure Boot medium. This is not an easy task, though. My Web page on Secure Boot covers the topic in moderate detail. In brief, you'd need to prepare a medium (a modified Ubuntu installer or a separate boot medium) that includes a pre-signed version of
PreBootloader.efi and that launches a boot loader (ELILO, GRUB, or rEFInd) that in turn launches the Ubuntu installer's kernel and initrd file. You'd probably need to enroll keys or hashes for the boot loader and perhaps the kernel and initrd file to get this all working, too. This is not a task for a newbie, though; to get this to work, you'll need to be comfortable with boot loader/manager configuration files, kernel options, and so on.