When R.C. Sherriff first wrote his play Journey's End, set in the trenches of the First World War, he had difficulty getting it produced, as theatre managers in the West End didn't want to show a play with no leading lady - a fact that later inspired Sherriff to title his autobiography No Leading Lady. Leaving aside the fact that it makes sense for a play set entirely in First World War trenches to have no on-stage female characters, was it really so unusual for the time for a play to have no on-stage female characters at all, or even no significant ones? Had there been any other such plays appearing in the West End before 1928?
It's pretty unusual but not unknown. A well-known play of the time with a virtually all-male cast was James Fagan's adaptation of Treasure Island, first performed at the Strand in 1922 and revived annually up to the beginning of WW2; there is one female role, and quite a lot of male pirates (going from the data in J. P. Wearing's The London Stage 1920-1929). Even the parrot is listed under the male actors. The tone is obviously quite different, though! This is a fun play to see with your children and not a harrowing depiction of soldiers facing death in the trenches.
Sherriff's agent may have been wary because of J. R. Ackerley's 1925 play Prisoners of War, which was critically acclaimed but commercially unsuccessful, closing after 24 performances. It had a predominantly male cast, and is better known these days for being one of the earliest mainstream plays to feature homosexual desire. Plausibly, the agent might have feared that audiences would not be too keen on a war play with a grim tone. While there were other plays of the 20s with a wartime setting, many of them were comedies (as indeed were many plays in general), as audiences were perhaps not too keen on depictions of their recent traumatic experience.
Following Journey's End, there were some more high-profile plays that similarly tackled the war, with an all-male cast. That includes Suspense (Patrick MacGill, 1930, at the Duke of York's) and B. J. One (Stephen King-Hall, 1930, at the Globe). Reviews of B. J. One noted that it felt like the Navy version of Journey's End, which perhaps shows that there were few other significant comparators.
To the general question, the vast majority of plays put on in theatres had mixed casts, including the most commercially successful ones, judging by the number of performances listed by Wearing. That encompasses original English works, perennial classics from Shakespeare, Sheridan, etc., and translated plays from Ibsen, Chekhov, and others. There are a few single-sex performances listed, most of those being charity productions or other 'specials'.
That is not the case once we broaden our scope to look beyond the professional London stage. The amateur scene was extensive, partly due to theatrical censorship which only applied in the case of public performances - if your audience was restricted to subscription club members then the Lord Chamberlain had no mandate. In any event, amateur theatrical societies put on a large number of plays, drawing from a different repertoire. Farces and comedies in general were popular, and there was a large library of possibilities - with their advertisement blurbs often emphasizing the possibility to stage them with minimal scenery, or subject to a cast restriction such as all-male. School and university groups would often be in a position of only having males available. As an example, Wearing records a 1926 all-male staging of Oedipus Tyrannus, done by a short-lived "Greek Play Society"; the sole female role, Jocasta, was also played by a man.