SQL Server 2012 Express SP1 install still not 11.1 I run the SQL Server 2012 Express SP1 install and it succeeds. After I have rebooted my computer, I do a 

select @@version


But still I only have version 11.0.21600.64. I have tried this on two computers now, still the same result.

The file I am running is: SQLEXPR_x64_ENU.exe downloaded from http://www.microsoft.com/en-us/download/details.aspx?id=35579
The full Express version (with SP1 included) is for installing a new instance, not for applying a service pack to existing instances. Sounds like perhaps you now have a second instance of SQL Express (no idea without seeing your configuration manager or services applet).

At this point you should download Service Pack 2 (not 1) to apply to existing instances, regardless of edition:

Download SQL Server 2012 Service Pack 2

(And perhaps clean up the extra instance, if in fact you did install a second instance inadvertently.)