Weird about the bills, but I guess we are on different packages. Are you UK based?
My electric - half the cost is the standing charge anyway. I have a smart meter so can see daily changes. There is very little, which does not surprise me as light bulbs use very little, nor do chargers, they run one wash a week, the cooker is used once or twice more a day, that's about it. What are your adult kids using for electric? Are they working from home?
Gas - heating a semi costs the same regardless of occupants. Again, standing charge is a substantial part of the charge. I guess a 6 bed where only one bedroom is heated vs 6 is going to cost more though.
Water - yes, definitely increases!
That's it.
I downsized as soon as mine left home but that's my choice, not their cost to pay or saving to make. Houses are a good asset investment. I wouldn't share my profit with them (well I would but that's not the point lol) so I don't expect them to contribute. Anyway, mortgage is paid so what would they contribute to in any case?
I guess op could just literally bill her child the difference in utilities bills as and when, between what it cost before and after. Smart meters are particularly helpful for that.