There's an excellent book about the immediate post-war period at VW called:
"Volkswagen Beetle - the Rise from the Ashes of War" by Simon Parkinson,
1996, Veloce Publishing Plc, available from either Amazon Books or Classic
Motorbooks.

In a nutshell, the British took over the factory in early May 1945.
Production was re-started shortly thereafter, with a number of Kubelwagen
being built from parts left at the factory. The factory was "repaired" using
tarps, poles, etc. to initially secure the interior of the plant from the
rain.

By September 1995, the British Military Government placed an order for
20,000 beetles to be produced for use by the Occupying forces, the German
Post Office, Red Cross, etc. Originally it was thought that the Kubelwagen
would be the ideal vehicle for these organizations, however the plant which
produced the Kubel bodies was in Berlin and under the control of the
Soviets, so the beetle was given the nod.

Car production resumed in late 1945. Here are the production figures for
1945-47 beetles:

1945 - 1,785
1946 - 10,020
1947 - 8,987

Ric