There's actually a similar but much more widespread talking point about gas, claiming the price of that is set on the international market and therefore the UK producing more gas locally would not help reduce prices. That should come with the exact same caveats (only to the extent that it can be imported and exported, American prices are much cheaper for Europe's because of this, and that's likely a big reason why electricity prices are much lower there) but the mainstream media unfortunately ignores them.

There is also a caveat that any cost savings from locality may be wiped out by higher costs in other areas. It may well be cheaper to invest in the US or Middle East and import as LPG. Transport costs are only one factor. And it is not like domestic supply would have no transport costs either. Running pipelines through rural England to fracking sites is not exactly cheap.