The Local Government (Household Charge) Act 2011 and the Local Government (Household Charge) Regulations 2012 provide the legislative basis for the household charge.
Section 2 of the Act sets out the meaning of "residential property" for the purposes of the Act. In particular, section 2(2)(d) of the Act provides that a building that is wholly used as a dwelling (other than a dwelling that forms part of a mixed hereditament within the meaning of the Local Government (Financial Provisions) Act 1978), and in respect of which local authority rates are payable, is not a residential property for the purposes of the household charge.
While I cannot provide a legal interpretation of the legislation, where there is a commercial premises on the ground floor and a residential property above it, and rates payable on the structure relate to the ground floor with the upper residential section benefitting from a rates allowance, that upper residential section is liable for the household charge under the 2011 Act.
The Act places the household charge under the care and management of the local authorities and application in particular circumstances is a matter for the relevant local authority. The household charge is on a self assessment basis, and interpretation of the legislation is a matter for legal advice in individual cases and ultimately a matter for the Courts.