It's The Local Authorities (Members' Allowances) (England) Regulations 2003. Para 24(b) specifies elected only.
It's worth reading the whole document, particularly in relation to the role of the Remuneration Panel (paras 27 onwards). Whilst the panel recommendations are not legally binding, the Council must publish a statement setting out the Panel recommendations and the Council's decision-making process in setting their allowance. I mention this because my local Panel recommended a maximum allowance of £50 per annum for each elected member other than the Chair, and if paying an allowance, however small, Councils must add every member to their payroll and deduct income tax where appropriate.