While German citizens were interned in WWII, refugees were exempted.
The
www.movinghere.org.uk archive has records of those exempted (mostly Jewish). There are a couple of hits for Kretschmer (but neither is E. Kretschmer or a Dr).
However, I think one of these might be related to yours - "J.K.M." (b. 1916 so there is a slight possibility he may still be living). He was b. Munchen (Munich), and resident Hartford, Cheshire, in 1940 when he applied for exemption. Notes say he was "not a refugee in the strict sense" but was Jewish, his mother and father had been driven out of Germany, and his sympathies were thought to be entirely British.
A newspaper article for "J. M. Kretschmer"'s marriage in the UK during WWII shows his father as Dr. E. Kretschmer (it is not clear to me if Dr E. Kretschmer was actually in the UK).
http://www.gda-old.bayern.de/findmittel/ead/findbuch.php?fb=830&lft=58&rgt=101341&id=53 - I wonder if this might be him?
Kretschmer Dr., Erich b. 14 July 1887 Lissa (Leszno, Poland)
wife "Philippine Bud." b. 12 June 1890 Dusseldorf
he was a chemist, Jewish. He had been investigated by the Munich police, and emigrated to Switzerland in 1937.
https://www.wiewaswie.nl shows that in 1939 Dr Erich, his wife, and a daughter b. 1921 ("Bazel" - maybe Basel, Switzerland?) were resident in Den Haag (The Hague) in Holland. His son may have been in the UK by then.