Labour could do well to introduce better ethical guidelines for political press.
Which will either get mired down in legal challenges, or ignored by all.
Once we are out of the ECHR (thanks Rish!) summary execution of editors who fail to fact check could be a thing. I suspect the media will very very quickly become pedantically accurate.
As with most things, there are some really simple steps that are available to start to tackle the problem. The fact none are taken is a clear indication that the powers that be don't think there is a problem.