You can still charge any fees agreed to before 1st June 2019. This is true until 1st June 2020. So for example, if any of your tenancy agreements have a clause saying that new tenants can be added to the AST at a cost of £xxx to the outgoing tenant, then you can still charge that.
If you are adding a new tenant to an ongoing tenancy, but the tenancy agreement contains no such terms, then you can ask tenant to pay them, but they could refuse.
If you are signing creating a new tenancy agreement, then you won’t be able to charge for referencing, etc., but you will be able to include a charge for amending the tenancy agreement. This could include adding a new tenant to the AST. You can only charge £50 maximum, unless you can demonstrate that your costs are above this and provide evidence to back that up.
More info in Part (2c) here: https://blog.openrent.co.uk/tenant-fees-ban-what-landlords-need-to-know/
Regarding an inventory, you should simply be able to update the inventory for the new tenant’s room, without having to do the whole property. This should hopefully keep the costs down!