Section 2(2) of the Act states:
“Trader” means a person acting for purposes relating to that person’s trade, business, craft or profession, whether acting personally or through another person acting in the trader’s name or on the trader’s behalf.
If you wish to challenge cuts to council services on the basis of their duty to do so, you'll first need to establish that such a duty actually exists. For example, local authorities aren't legally obliged to provide public toilets, so there can be no legal challenge to a decision to close them. However local authorities are obliged to provide public library services. [Libraries and Museums Act 964. See here:
https://www.gov.uk/government/publications/guidance-on-libraries-as-a-statutory-service/libraries-as-a-statutory-service ].
Some other statutory duties of local authorities are given here:
https://www.bbc.co.uk/news/uk-45129167