Thanks John for identifying the Bedford!
On the Haagse Beeldbank another photo of the same vehicle has become available:
http://www.haagsebeeldbank.nl/hga:col1:dat335307
According to the Irene Brigade vehicle list, the vehicle number was L1284766, the chassis number MW19426 and the engine number 16685.
Another photo shows a 1939 or 1940 Ford which was part of the brigade HQ:
http://www.haagsebeeldbank.nl/hga:col1:dat246076