Why would I care if you brought your landlord wine? Surely I should get the wine?
Being realistic, I don’t see any easy way for you to compel your landlord to perform this work. Maybe offering a compromise where they pay for the new part but you install it could work?
But if you report a dirty detergent tray and rubber seal to your local council’s environmental health team, I guarantee they will not be sending the landlord an enforcement of repairs notice.
Tenants are expected to treat the property and its furnishings in a tenant-like manner, and that presumably sometimes means cleaning things (e.g. fixtures and appliances) and replacing things (e.g. lightbulbs).
Offering a compromise might be the best way to proceed.