Since the Republicans were socialists from the beginning (of the big business variety), there was no one left to defend small government anymore.
Wilson, who in my book was the worst President ever, then gutted the Constitution with the 16th through 20th amendments, established the Federal Reserve Bank, and got involved in a European war while running roughshod over American liberty at home.
This led directly to the all problems of the twentieth century - the rise of socialism and totalitarianism. While Wilson has a lot to answer for, it's probably true that it was inevitable. If he wasn't there, someone else would have done it, just as someone else would have done what Bryan did. They were simply responding to the temper of their times.
Unlike American Democrats, the British Liberal party never sold out. So Labour took their place, giving the Brits one big business party and one socialist party, just like in the US.