Your first sentence is rubbish, in more than one way. Opening a window is not much work and doesn't cost more than running a dehumidifier. I know this because I have tried and compared both methods and I keep a detailed log of my energy usage.The energy you use for venting your house every day would cost a lot more than £200 a year of food to compensate. So, you put in the work and still end up paying more.
To bring a room from exterior temperature to normal room temperate would probably cost 10x 50w of gas.
A 50w dehumidifier is not going to bring a room from exterior temperature to normal room temperature either, so this is not a valid argument.