score:8
I suspect that we have a conflict of assumptions and language. The Lord of the World is a work of speculative fiction. None of it is historical. @KillingTime pointed out the key to understanding the entire question; the novel was published in 1907, so it isn't based on historical events at all. It is speculative fiction about then (then) future.
in 1917 the Labour party gathered up the reins [in England], and Communism really began
I haven't read the novel, but I take this to mean that in the novel, the Labour Party won the general election in 1917 and assembled a parliamentary majority. The statement is neither true nor fictional - it is about what was (in 1907) the future - it is speculative.
Likewise for the second quote - the author was writing in 1917 about the (then) future.
The new order began then; and the Communists have never suffered a serious reverse since, except the little one in ’25. Blenkin founded ’The New People’ then; and the ’Times’ dropped out; but it was not, strangely enough, till ’35 that the House of Lords fell for the last time. The Established Church had gone finally in ’29.”
I infer that the Communists held a majority in the House of Commons from that point forward - although in 1925 they might have had to form a coalition with another party. Blenkin and the "new People" are a fictional invention. Wikipedia clarifies that in the novel, the House of Lords was disestablished in 1935.
The Established Church is probably a reference to the Church of England. Communism's position about the church is well known; Wikipedia clarifies that in the future described by the novel,
The Anglican Communion has been disestablished since 1929 and, like all forms of Protestantism, is almost extinct.