You pay council tax which includes an amount for domestic waste and landfill tax, the business doesn't pay this.
But yes, in your example it is the same rubbish and could belong to the same owner but there is no way of doing this without large industry being able to dump huge amounts of rubbish free of charge and the public would also be paying for the landfill tax.
I'm sure if someone could come up with a more credible solution then there would be a lot of ears. Bearing in mind that some business produce a lot of waste and some don't.
As an aside - poll tax was a lot fairer than council tax (the number of people in a house is roughly proportional to the amount of waste) but the media got its teeth in and demolished poll tax.
In a time of universal deceit - telling the truth is a revolutionary act. George Orwell
When the debate is lost, slander becomes the tool of the loser. Socrates