About a year.
XI happens around 2258.42 if I remember correctly, Spock mentions it in his log after Vulcan's destruction. In STID we see the date in London as 2259.55, at the beginning of the movie.
In these movies the number after the . indicates the day of the year out of the 365 days. So from dead Vulcan to couple waking up in London 378 days had passed.