Heating elements (kettles etc), also don't care, and a lot of motors used in household items are universal motors[1], which will end up running at the same speed even as the frequency drops. Old alarm clocks do use the mains supply as a time reference though, so they will end up having the wrong time, as happened recently in the European grid [2].
For a transformer, efficiency decreases rapidly[3] with falling frequency. For household usage, transformers running directly on mains frequency are only used for linear power supplies (as opposed to the SMPS supply used earlier) which found in things like audiophile level power amplifiers (adds a nice bit of weight), so your Class-A amplifier may get even hotter.
The power grid uses transformers of course, to step down the several kV supply to the 240V used in the UK, and its possible that a big enough frequency shift could cause overheating of these from the decreased efficiency. I would be very surprised if they would not turn off if they got too hot though, it seems like a sensible thing to design in.
In short, not much for small changes, but the frequency is falling as there is more consumption than supply, so the supply gets turned off to decrease demand.
[1] https://en.wikipedia.org/wiki/Universal_motor [2] https://www.irishtimes.com/news/world/europe/clocks-in-25-co... [3] https://electronics.stackexchange.com/questions/23999/effect...