It's hard to say. I'm not an expert on British politics so I can't say definitively how his victory would affect things there. I think it would majorly depend on how successful he or other reformists like Sanders were, and what the necessary reaction would be like.
If we use FDR as an example, his reforms both improved the station of the working class, but also placed the US govt in such security that they were able to decimate the revolutionary element that made those reforms possible and necessary, and we're towards the tail end of them being rolled back now. If global socialist revolution was a real threat in the 20s and 30s, then FDR's reforms contributed to delaying it for nearly a century.
However, neither Corbyn nor Sanders are FDR, and the 1920s are going to be as different from the 2020s as they are similar. We can't just look back and say "this is how things are going to happen."
If Corbyn or someone like him did succeed in overtaking political power and were able to institute some of the reforms that they are after, the lot of the working classes would be immediately improved, if just a little. This might placate some, but I don't believe that most are in such comfortable positions that they would be satisfied with or even desire a return to the status quo. To satisfy the working class in FDR's day required a major reconstitution of American society. Take the transformation of the Tennessee valley, for example: en.wikipedia.org/wiki/Tennessee_Valley_Authority
Could we see something today on such a massive scale? It's not impossible, but I doubt it.
I think that whatever progress or improvements might be won would be dismally short lived, either because they fail to anticipate rapidly developing economic situations, environmental disaster, or outright political or industrial sabotage. I strongly suspect that even if progressives were able to win office, the various other limbs of bourgeois government would conspire to thwart their reelection and their programs.
However, we see here a very big rub. People are already angry, and getting angrier. There's a good chance that political defeat would knock the wind from this growing sentiment, but I think there's an even better chance of it inflaming political action from below. This is why they are so desperate to keep people like Sanders and Corbyn out, because keeping people from getting what they want makes them mad, but giving people what they want and then taking it away makes them
There are far too many factors at play to say definitively one way or another, but this is what they fear, especially because the bourgeois are rapidly running out of excuses to not give people what they want, and were they to get it only for it to be taken away, the blame and the shadow of guillotines would fall squarely at their feet.