If there is another election, why would JC affect it? I don't think there will be any affect unless he and labour propose policies that will affect it.
They don't have control over interests rates (well, I guess they can exert pressure on the BofE). So, that tool is gone.
I don't think they are likely to introduce any capital controls in the way of restricting foreign ownership.
The best I can see from them is perhaps more council houses being built (that is a maybe) which will help prices come down slightly, but will be cancelled out by more housing benefits (pushing prices up). So I think net will be to push prices higher.
The other thing they might encourage is high tax on empty homes. The lack of this is excellent evidence that neither Tories nor Labour are willing to do anything about house prices.
The problem is that both parties, and the population in general, now are in a huge pickle. What everyone wants is for prices to stay high (to keep owners happy) and houses to be more affordable (to keep non-owners happy). Guess what? Those aren't compatible. You can read about the "affordable" housing being built (usually at 500,000+ price). Given the complete disconnect in London with local wages, the only real solution is a severe crash, and the government will do anything they can, until it complete runs out of their power, to stop that.
In short, I don't think JC matters unless he is proposing a radical policy.