> Inflation is a measure of the cost of living

The faster your cash loses value, the stronger your incentive to trade it for something else. That something else can be financial assets.

> It's not got loads to do with large-scale, institutional investments

For investors, particularly retail investors, the consumer price index is most relevant. But for whatever it's worth, producer prices are up over 16% in April (7% excluding "foods, energy, and trade services," which jumped over 50% annualized) [1].

To be clear, I'm floating a hypothesis here. I have seen no evidence linking inflation to demand for these companies' shares. (If anything, it should be the inverse.)

[1] https://www.bls.gov/news.release/ppi.nr0.htm

That depends. Inflation is a measure of the cost of living in terms of currency. It can be high either if goods and services required for living become scarce, or if currency supply increases. Currency supply increasing does affect asset prices.

Inflation then is already higher. Cost of living is driven mostly by rent