All regions of the world come with the pre-installed laminate sheet over the glass, however that is NOT a screen protector. Only the European unbranded units come with a screen protector in the box. So if you brought a carrier branded unit or an unbranded unit from say Hong Kong or Asia you will not get th screen protector, but say you buy an unbranded unit from Clove or Handtek in the UK you will. Here is what Sony support said about the screen protector issue:
The scratch resistant screen is covered in a non-scratch resistant anti-shatter laminate sheet that will reduce the likelihood of the screen cracking or shattering. This is NOT the top layer intended as the laminate sheet is very easily scratched and attracts lots of dust and fingerprints. You are then supposed to put a screen protector over this laminate sheet which will do a much better job of resisting dirt, fingerprints and scratches than the laminate sheet. One is included in the Xperia packaging in unbranded models. The preinstalled laminate sheet is glued down. It can come off but it will leave a glue residue on the screen that is not easy to get off. The second layer screen protector included with unbranded models just bonds through natural static adhesion onto the laminate sheet rather than a glue.
The laminate sheet can not be replaced on its own after removal from the screen. The laminate sheet is bonded to the screen with heat as part of the production process in order to properly fuse to the glass and give it its anti-shatter properties. The laminate sheet is not sold on its own as a part and the only way to replace a damaged or removed laminate sheet is to replace the entire front screen glass panel assembly. As such Sony highly recommends you immediatly install the screen protector included with direct from Sony unbranded Xperia models or purchase a commercially available screen protector for carrier branded units.
PS. If you did not get a screen protector in the box or you messed it up, Handtec has the same OEM ones that come in the boxes in two packs. The one for the Xperia U is available here: