@Joe Shearer @Ssan
Ishtiaq Lahori Sb has also replied, though his reply wasn't very useful. He wrote:
"You read my Jinnah book, the reference is given there."
I obtained a copy of Ishtiaq Sb's book, "Jinnah: His Successes, Failures and Role in History," and on page 473, he references the same article by Dr. Ayesha Siddiqa from The Friday Times that we previously discussed. Ishtiaq Sb mentions that Dr. Ayesha was kind enough to share with him the original note of the UK high commissioner, which is archived at Kew Gardens under file number DO 142/476. What is interesting, however, is that Ishtiaq Sb attributes the content of the letter not to Dr. Ayesha herself, but to "Jinnah, Pakistan and Islamic Identity: The Search for Saladin," a book I went through, but couldn't find any mention of the alleged letter. However, the author of the book, Akbar S Ahmad, does mention Jinnah's meeting with Al-Banna. I have also brought this apparent mistake to Ishtiaq Lahori Sahib's attention, let's see if he responds.
It doesn't seem like we'll make any progress by reaching out to the authors who are being evasive. So, to settle this debate once and for all, I have requested a copy directly from the British National Archives. They have said it will take about two weeks until June 20th to get the copy sent to us.