If you weren't there to experience the Blitz and its aftermath, then this is probably as close as you would like to get. The German V1 rocket seen flying overhead places this film in the last 12 months of the war, and the citizens of Southwark appear well-practiced in picking up the pieces of their decimated neighbourhood. By the end of the film the worst is over, as the Royal family are driven through crowd-lined streets and kids enjoy a victory party.
The road at the start of this film is Park Street, which runs perpendicular to Southwark Bridge Road, and it's probable that the damaged flats are on either the Peabody or Sumner estates nearby. The nurses were likely from Guy's Hospital.
Many thanks to London Topographical Society member Mrs Joan Horton for her assistance in identifying these locations.