Cloth Shoulder Badge, Bromley with Red Cross

[geezer#199]

I was going through my father in laws military accoutrements the other day and came across the attched shoulder patch. I have no idea who it represent other then I feel it is from England. He joined the war effort from Canada, 17 RCA, in 1939 and traveled to England landing in Gourock, Scotland. They then traveled to Aldershot for training. He was in Africa, Italy and Belgium as well.

If anyone can identify this badge for me it would be much appreciated.

Thanks in advance