As you can see, this Beit Midrash was opened from 6:00 AM to 12:00 AM daily (I assumed that 12:00 PM is a mistake). Anyone could learn there at any time. There were constant minyanim, to accommodate those wanting to say kaddish. In addition, it was responsible for creating a school for children (where "they now teach Gemora for one hour a day") and numerous charities for the poor and for women. It provided a place for poor people to take shelter and warmth. He contrasts it with another Beit Midrash which is only open for a few hours in the evening (and the gas lights go out at 9:00 PM).
Not mentioned in the letter is that the Beit Midrash which Cohen founded in 1879 actually encompassed even more than what he outlined. For example, attached to it were public baths for the poor, who presumably had nowhere else to bathe. Cohen established a fund to aid persecuted Jews in Russia, for which 100,000 were raised. Initially three hot meals per week were provided for as many as 200 people, but the amount was raised to five. Cohen petitioned the Shah of Persia and the Pope in Rome to assist persecuted Jews. It took steps to promote Shabbat observance. It took on landlords who were raising rents to very high amounts in the (poor) East End. In addition, Cohen cultivated good political connections, especially with the British royalty.
See A review of the work and correspondence of Simon Cohen, on behalf of the East End Jews and the Beth Hamedrash Lomdi Torah (1901).