I was under the impression that not all the despicable experiments done by Nazis were known at the time. This history stackexchange post is inconclusive whether Churchill referred to military prowess or Dr. Mengele's experiments.
Churchill most definitely did not meant experiments made by Dr. Josef Mengele in Auschwitz and it is nigh improbable that he mentioned German Nazi experiments at all. Unless he could foresee the future, that is.
The 'Finest Hour' speech was made on 18th July 1940. At that time, Dr. Mengele has not joined Waffen-SS yest and was stationed at Kassel in the capacity of a regular medical officer. His scientific work focused on anthropometrics with no racist or eugenic undertones (anthropometrics was a popular topic back then, given quick development of anthropology and archeology*). All in all, there was nothing that would have indicated that this doctor will turn into 'Angel of Death' in the matter of few years. As a matter of fact, the first transport of prisoners (roughly 750 people, mostly Polish political prisoners) arrived in KL Auschwitz on 14th July 1940, four days before the 'Finest Hour' speech was delivered.
The most widely known Nazi experiments, i.e. twin experiments in KL Auschwitz were conducted mainly by Dr. Mengele between 1943 and 1944. Sterilization and fertilization experiments conducted on over 300 000 subjects, primarily in KL Auschwitz and female KL Ravensbrück under the supervision of Dr. Carl Clauberg started in early 1941 and lasted almost until the end of war. One of the first grossly unethical experiments using prisoners as unwilling subjects were temperature and pressure tests conducted in KL Dachau on the behalf of the Luftwaffe by Dr. Sigmund Rascher, Prof. Ernst Holzlöhner and their coworkers also began in 1941. Tests on Russian prisoners of war made to determine whether there the Russians were genetically conditioned against cold were also conducted only after the Eastern campaign stalled (early 1942).
Most lethal experiments, where subjects were expected to die or were left to die has been conducted only after the Wannsee Conference on 20th January 1942, when the decision of a nationwide genocide aimed at total elimination of Jews and Gypsies (Romani and Sinto) in Germany and conquered lands has been made. With concentration camps turned into extermination centres, murderous experiments could have been conducted with little to no opposition. Majority of such procedures (exposure to mustard gas or poisons, infliction of wounds, starvation/dehydration) has taken place mainly between 1943 and 1945, primarily in KL Dachau and KL Buchenwald.
Summing it up, the term 'perverted science' used by Churchill was almost definitely not a reference to human experiments in concentration camps and death camps as they were conducted (not to mention exposed) several years after the speech. If anything, he was referring to general racist and elitist attitude prevalent in Germany after 1933 that used scientific explanation to justify the racial or eugenic policies such as Nürnberg Acts of 1935 or elimination of congenitally ill and developmentally challenged people as well as psychiatric patients, also known as Aktion T4.
*This would be also a prime example of 'perverted science' where the methods developed for identification of skeletons and determining origins and movements of various ethnicities (basically the only way of doing that prior to the advent of modern genetics) were used to identify 'undesirables'.
[1] Gerhard Baader, 'Menschenversuche in Konzentrationslagern' (in: Johanna Bleker, Norbert Jachertz (red.), 'Medizin im Dritten Reich', Deutscher Ärzte-Verlag, 1993).
[2] Yves Ternon, Socrate Helman, 'Histoire de la medecine SS', Casterman 1969 (I used 1973 Polish translation, not sure if English translation exists).