I am mostly referring to the Ford Anglia, but the design was continued 1953-59 as the Ford Popular. A four-door variant produced 1939-1953 was the Ford Prefect. The Anglia and Prefect brands were continued into the 1960 following a complete redesign not covered in this post.
Not having grown up in England, and given the similarity of the cars shown below, I'm hoping that I'm correctly presenting the model years and model names for the images below.
The Anglia name appeared on this car in the Fall of 1939, but the redesign of the Y line was produced starting with 1938 models.
It seems Ford was still making cars in England in the year after World War 2 started. Note the changed grille -- retro compared to the more aerodynamic looking 7Y grille, above.
The three-element grille was used for only one model year, according to one source. Click to enlarge a little.
The Anglia front has reverted to pre-1940 7Y form.
Ford featured both brands in a number of advertisements and brochures around this time. The Prefect was more expensive and featured four doors instead of two and had a different grille, fenders (wings) and trunk (boot). But otherwise the cars were essentially the same. Click to enlarge.
Compare to the 7Y photo at the top. This design was continued through the 1959 model year even though it was thoroughly out of date.
There really isn't much to say about Anglia styling. The "package" was small and Ford stylists shrunk circa-1936 American large-car styling features onto it. Moreover, because it was an entry-level automobile, it was designed to be manufactured for the lowest possible cost. Perhaps that is the reason for those odd little headlamps perched on the fenders; with a larger budget, they might have been better integrated with the rest of the styling.