I think this may be the pitch to which he's referring:
This Hebrew reference notes that the field was home to first the British Police (so maybe mentions it) and four other teams.
Maybe Douglas Duff mentions it in his books -
1. Sword for Hire. The saga of a modern free-companion, etc. 1934.
2. Galilee Galloper. [A biography of Edwin G. Bryant, known as “Abu George,” formerly superintendent of the prison at Acre.] 1935.
3. Hammer of Allah. 1936.
4. The Horned Crescent. 1936
5. Palestine Unveiled, seemingly a reissued book or collection of the above four books.
This article also contains relevant information, including:
The British Mandate warned about the expansion of the national tendencies of the social athletic clubs, Filastin in April 1921 published this excerpt:
Last Saturday was the inauguration of the cornerstone of the Sports Club in Jerusalem. The Palestine Weekly mentioned that Mr. Stores, the Governor of Jerusalem, insisted on the participation of everyone regardless of his religion or beliefs.
Sport was used as a cover for paramilitary activities especially by the Betar organization. Under the title (Jabotinsky’s Program: “Shooting” a Jewish army was initiated under the cover of clubs). Filastin published a translated article from the newspaper Ha-Mishkov that talked about the question of Palestine, It was argued in the article that establishing a military unit was difficult in the circumstances but imperative and sport clubs for youth could serve as a venue for military training.19
During that period, Filastin published a number of articles about Maccabi and Hapoel clubs, including accounts of their trips to Syria and Lebanon which indicated that the goals of these trips were to sustain the relationship between the organizations in these three countries.20
One of these articles under the title “ Insulting the Zionist Flag” described an incident when the Hapoel Club won a football match in Damascus. Its fans were carrying the Zionist flags and singing their national songs. This display provoked the Arab crowd and a fight broke out during which the Arab fans tore the Zionist flag.21 Also, some news was published about skirmishes between Jewish and Arab fans during the matches because of the bias of the referees.22 Most of this news carried a nationalistic undertone and aimed to reveal the rejection toward the Zionist project and its policies towards Palestine.
Starting in the 1920’s, Jewish clubs in Europe and the region began to come to Palestine to compete with Jewish clubs. They flew flags that resembled the Zionist flag, a provocation that local Arabs vigorously protested against to the British authorities. The executive committee of the Muslim and Christian Association sent the High Commissioner for Palestine protested against the flying of the Zionist flag at a football match held in Jerusalem on January 12, 1925, asking whether the ordinance regulating the flying of flags issued by the Government of Palestine in August 1920, had been abrogated.23