It would go some way to mitigating it temporarily, very short term, unless of course you just want to throw 20 billion plus at the problem every few years. I'm not convinced by the inflation argument simply because I'm not convinced the current inflation rate rises have as their cause recent activities (COVID, Ukraine etc) the causes are more long term, and inflation over the last twenty years or more has been artificially suppressed, also inflation and cost of living are not as connected as normally portrayed. To illustrate; the cost of living crisis has been with us since I would say the late 90s, the availability of very cheap credit at every point in the supply chain from extraction to end consumer has masked the cost of living increases, but there comes a point (now) when there is a perfect storm of events that turns what is an economy functioning at the very edge of functionality to one that is collapsing.
New players came onto the market whose primary revenue generator isn't supplying energy, they are leveraging futures and other energy markets and often using energy in the financial system in typical financial system ways. That has provided "competition" based exclusively on the consumer price, so all companies have to bring down charges to stay in the market which forces more of them into speculative activities. These speculative activities brings development to very short term points of view in that the infrastructure and its potential failure is just another point on the speculative risk graph, which can be mostly ignored until near failure. When near failure arrives if they even see it arriving the money behind simply bails out.
I was advocating a while ago for de-profitising (not nationalising) energy and other utilities amongst a few other things, the problem with that is the energy companies and their core profitability are a biggish part of pension plans for workers, so a wholesale de-profitisation programme hurts primarily workers in the long term as much as nationalisation would. The models I have looked at all predominantly impact ordinary workers / people either directly at point of implementation or further down the line even when the changes are specifically designed to help them. The actual act of Starmer's proposal would do little more than prop up a broken industry for another decade.
The issues about rising energy costs get highlighted every few years, but its always seen and analysed as a temporary crisis, and the basic system, as in finance and a couple of other sectors just weathers the immediate storm whilst conditioning the public to a new normal.