Birksted flew Mustang III, not IV, during his time as Wing Commander in Bentwaters Wing. He also carried out operations on the Hurricane and on Spit I and II in the early days of his operational career.
The number of victories credited to him depends - as is mentioned - on the sources, including on how you interpret some of his combat reports.
For more in Birksted
http://www.danishww2pilots.dk/profiles.php?person=15
I have redesigned my website recently. The page on victories has not yet been redesigned and is therefore offline at the moment. When on-line again, it includes a transcript of all combat reports on Birksted's victories.
Mikkel