I thought I would check what the Socialist Standard of the time said about that demonstration on 18 November 1910 on which the musical is based.
Nothing as it happens because the December 1910 issue was taken up with the general election that month. There was an answer to a question about the franchise, saying that enough workers already had the vote for a socialist-minded working class to win control of political power, prefacing this with “The Socialist Party is not opposed to Adult Suffrage”.
The demonstration was not in favour of votes for women but for votes for rich women only (Votes for Ladies, as it was known as). Here is how Wikipedia describes the Bill they were demonstrating in favour of. The MPs behind the Bill
“proposed legislation that would have enfranchised female householders and those women that occupied a business premises; the bill was based on existing franchise laws for local government elections, under which some women had been able to vote since 1870. The measure would have added approximately a million women to the franchise; it was kept to a relatively small number to make the bill as acceptable as possible to MPs, mostly Conservatives.”
https://en.m.wikipedia.org/wiki/Black_Friday_(1910)
I wonder if the musical brings out that point.
It is probably not without significance that after the much wider but still limited extension of the vote to women after the War, Emmeline Pankhurst became a Tory and had been adopted as a candidate for them just before she died in 1928.
That the Suffragettes struggled for votes for women is one of the biggest political myths of our time. Their official policy was votes for women on the same conditions as men. At the time about a third of men didn’t have the vote either. So perhaps as much as half of adult women would still have been left without the vote.
Sylvia, on the other hand, was for a while a Left Communist who clearly understand what socialism was. Even before that, unlike her mother and sisters, she campaigned for adult suffrage.