An additional segment to feature the theme tune itself had originally been planned but was dropped for timing reasons. However, a video montage did accompany the TARDIS within the Queen track during the technical rehearsal, though it appears to have been dropped for the live ceremony broadcast (available via BBC iPlayer until the 4th August, at about 1h01m10s). Doctor Who's brand manager Edward Russell clarified:
A video montage which very briefly showed all 11 Doctors was approved but we were told it may not be included which was clearly the case.
In Doctor Who lore, of course, the ceremony saw the Doctor himself light the Olympic Flame (Fear Her, 2006). In reality, the Olympic Cauldron (made up of 204 copper petals representing every country competing at the Games) was ignited by seven aspiring young athletes chosen by British Olympic champions.