This thread is crazy!
OP, think of the costs that you incur a) specifically because your daughter and b) you would incur anyway but are higher because of an additional adult.
For example, are you including your daughter in the grocery shopping and cooking or does she have to buy and cook her own food? The first is more likely so think how much you spend on food and divide it by the number of people in the house. Your daughter should be paying you a portion of that.
I assume that you have internet access that your daughter uses because that is considered a modern day utility bill. Your daughter should pay a portion of that.
Water rates or water meter? Most people are on a meter now so think about what proportion of that bill you use versus what she uses and what everyone else in the house uses. The number of times she runs the washing machine compared to everyone else and long, hot baths in comparison to short, sharp showers.
Electricity. Slightly trickier. You would be baying a fair but just to keep the house going with standing charges etc. But more people also mean more usage. So perhaps this bill should reflect that rather than a % based on household size. But still something to consider especially if she has as many devices charging as most young people today.
Council tax - does she pay this? Do you pay this? She should be contributing towards this.
Finally, the rent. A small contribution would be appropriate from an adult whether they are employed or not. It doesn’t matter whether or not you would downsize if she wasn’t living with you.
I’ve got to say that, if you are including food and everything else I mentioned, I think £450pcm actually sound pretty reasonable.
However, if you want to know whether or not it is reasonable,e, do your own calculations and see how much profit or loss you are making way charging your daughter. Then decide whether it is appropriate or not.