Have you turned both secure boot & fast boot off?
You will need to use the 64 bit version of 12.10 and from the UEFI menu boot the flash drive in UEFI mode. That way it will install in UEFI mode.
Systems need quick boot or fast boot turned off in UEFI settings. Vital for some systems. Best to backup efi partition and Windows partition first.
Use Windows Disk Tools to shrink Windows main partition, but not to create any new partitions, if installing on same drive.
As of 12.04.2, it is possible to install on UEFI systems with Secure Boot enabled (using signed versions of Shim, GRUB, and the Linux kernel). This is only currently set up for Ubuntu (desktop, alternate, and server) and Edubuntu images due to pressures of time; we expect to enable it across the entire Ubuntu family for 12.04.3. Details:
You need Boot-Repair or manually update grub's efi entries as per bug report.
grub2's os-prober creates wrong style (BIOS) chain boot entry
type of entry from Boot-Repair that should work.
'Windows UEFI loader'
Type of entry that does not work:
'Windows ...) (on /dev/sdXY)'