Make sure you boot the Live CD in UEFI mode by looking for the entry that looks like [UEFI] USB Flash Drive or something similar. Then you can partition everything yourself, but make sure you make one partition formatted as ext4 which has at the very least 700MB of size and mark it as /boot-partition. Then create a partition of size ~400MB, format it as FAT32 and mark it as EFI-partition.
And of course you have to make sure the root-partition has enough space anyway.
Also you should make sure to change the partition table to GPT.
But beware of one thing: the first step is crucial. If your machine does not support EFI, then it won't work. You have to make sure to choose the entry saying something like:
[UEFI] USB Flash Drive.