Is Uriel Septim Breton or Imperial ingame? I wonder because in lore Tiber Septim was most likely Breton.

Imperial.

Imperial, the line of Tiber direct descendant has ended way before it reached Uriel Septim VII.

In game the Emperor is an Imperial

The actual dynasty tree is shown here. You can see there is a rather wide separation from Uriel Septim and Tiber Septim.

http://www.uesp.net/wiki/Lore:Septim_Dynasty#Tiber_Septim

Maybe someone in the Lore forums can better comment on the race(s) of the Septim Dynasty. I'll see if a moderator wants to move this thread.

Who knows? The Emperors are likely to have illegitimate secret sons....

In ES, a child is the same race as their mother, so it all depends on the women in the bloodline. One of them - Katariah - was a dark elf in fact, which made her sons Emperor Cassynder and Uriel IV dark elves as well.

Tiber wasn't a Breton. He was a Nord born in Alcaire.

Apparently Emperors after the Elven blood was introduced aged like Bretons... Of course, this was probably watered back down to Imperial.