Why do older images of nurses' uniforms have a red cross?

The nurse depicted in Banksy's Game Changer artwork bears the red cross emblem - but why?

Red cross nurse uniform hi-res stock photography and images - Page

1930 Press Photo Society Rehearses For Annual Charity

1940s nurse hi-res stock photography and images - Alamy

Vintage Pictures of Red Cross Nurses' Humanitarian Aid Worldwide

Red cross nurse uniform hi-res stock photography and images - Alamy

1940's nursing uniform American red cross, Red cross, Vintage nurse

I love the cross across her chest. Back when nurses looked like

The history of our movement

WWII Red Cross and Army Uniform Exhibit – The Pragmatic Costumer