Other tabloids agree that Charles Coward was discredited but none are forthcoming about who did the discrediting. Having now checked numerous sources, I can't find any substantive corroboration of his stories, but I did find some monologues skeptical of him. The best is
British POWs and the Holocaust by Russell Wallis. He begins by comparing against one another Coward's biography, his affidavit, his testimony, and two earlier reports that he wrote in 1945. A familiar methodology to users of this forum. An early summary of this analysis appears on page 134:
Thus far, it can be seen that Coward had possibly falsified his rank, provided three different dates for joining the army, made two different but equally implausible claims about sabotaging the transport of V1 weapons and suggested that the smoking chimneys of Auschwitz could be seen and smelt from a distance of nearly 100 kilometres away. Such claims are fairly harmless in and of themselves however, they provide a backdrop [...]
That's just the beginning. Over the following 37 pages, Wallis systematically debunks every aspect of Coward's story.
On the tales of saving Jews by exchanging them for dead bodies, Wallis shows that these stand in contradiction to the claims of other witnesses at Monowitz and are generally implausible. (p.160)
Coward also makes an astonishing claim about Birkenau which I think is best summarized by a writer for Return Ministries, which is an aliyah organization, on
this old webpage:
Charles Coward of England was known only by his code name, the Count of Auschwitz, during the holocaust years. He was very instrumental in Felix [Opatowski]'s life and together with other men and women, they were part of a courageous underground resistance team who were successful in smuggling dynamite into Auschwitz and Berkenau. They blew up two of the crematoriums thereby saving thousands of Jewish lives.
Therefore we have Coward to thank for erasing the evidence of mass murder. This is a real story from Coward's biography, but Wallis points out that it is found
only in his biography, not in his other accounts. Also as part of this tale, Coward claimed that there were Sonderkommando cellars inside IG Farben which the Sonderkommando stored corpses in prior to incineration. This has no basis in fact. (p.158)
I must also include this choice anecdote (p.135):
He informed British officials that, during a visit to Gleiwitz in August 1944, he had observed some very peculiar activity. He ‘noticed that some Germans were training wearing a peculiar mask’, but could not understand what was going on so decided to make some ‘discreet enquiries’. The incredible explanation given to Coward was ‘that they were experimenting or training with a new shell that when exploded froze everything in a mile radius.’
A freeze bomb!

Since this story was in the same region as the story of
20,000 Jews vaporized by an atomic weapon, perhaps they have a shared origin.
In his final estimate, Wallis describes Coward as having "quite remarkable audacity", especially for "his bold but ultimately unsuccessful attempt to hold fast to what was, as shown above, patently untrue courtroom testimony". He calls the version of Coward presented in his biography "a semi-fictional character" created by its authors for the British public "who were keen" for just such a story. (p.166) Lastly, "if all the available evidence is considered, then Coward’s story is too full of holes and contradictions to be taken seriously in the context of modern Holocaust scholarship." (p.167)