Improvement Notice Fee: any legal basis for LHA to charge this?

HMO Licensing

I have received a letter from Portsmouth City Council saying I will be charged a Fee if they issue an Improvement Notice under Part 1 of Housing Act 2004. I know LHAs can recover expenses in cases where they are directly involved in effecting remedial actions (Schedule 3), but I can find no basis for them to charge a Fee for execution of their Part 1 duties. I think PCCs Fee is £587 and I've found similar published on other local authority websites. I'd like to know what legal basis they might be relying on for charging such a Fee. Any ideas? . Anyone else had this? Any tips on how to respond?