How is Spitfire landing gear powered?
Early models of Supermarine Spitfire (prior to the 175th production aircraft) had no hydraulic gear extension system, according to Wikipedia:


  At the same time the manual hand-pump for operating the undercarriage
  was replaced by a hydraulic system driven by a pump mounted in the
  engine bay


Source

The movie could show the normal extension of the undercarriage, using a lever, but a lost engine would not impact the operation.



After the 175th aircraft, the gear was hydraulics powered, so without engine running, the pressure could be insufficient. The design included an emergency extension using a $\small \textrm {CO}_2$ cylinder:


    


Source: 1940 Spitfire Manual

The system is visible on this image (black bottle with red handle "Emergency Only"):

  

Source

The hydraulic gear control box is at the center.