Is my landlord's house in multiple occupation rules code of practice binding on him?

A code of practice is a set of recommended standards. The Act allows the government to approve one, but the Act also says that breaking it is not, by itself, unlawful: "A failure to comply with a code of practice for the time being approved under this section does not of itself make a person liable to any civil or criminal proceedings." [cite:uk-housing-act-2004-sec233] In plain terms, the agent is right that this code cannot force a repair by its own force. The 14-day figure is the agent's claim about the code, and the sections provided do not confirm that any such deadline exists. Separately, the Act allows binding rules. Regulations may "impose duties on the person managing a house in respect of the repair, maintenance, cleanliness and good order of the house and facilities and equipment in it" [cite:uk-housing-act-2004-sec234]. Breaking such a regulation is an offence: "A person commits an offence if he fails to comply with a regulation under this section." [cite:uk-housing-act-2004-sec234] The provided sections do not list the actual regulations, so I cannot say whether they cover your boiler or your bins. You need to check which regulations are in force. Whether these rules apply to your house depends on the HMO definition. Your house may meet the standard test, which requires that "the living accommodation is occupied by persons who do not form a single household" and that "two or more of the households who occupy the living accommodation share one or more basic amenities" [cite:uk-housing-act-2004-sec254]. From your question, six people share one kitchen and two bathrooms and pay rent, but the sections also require occupation as a only or main residence, which is not quoted here, so this is an assumption to check. The Act also lets prescribed standards cover "bathrooms, toilets, washbasins and showers" [cite:uk-housing-act-2004-sec65]. Those standards are set by regulations made by the national government, not by the council. The council then uses them when judging whether a house is suitable for a given number of occupants [cite:uk-housing-act-2004-sec65]. Whether two bathrooms are enough for six people depends on those regulations, which are not provided. Uncertain points: the sections do not set a repair deadline, do not say who must fix the boiler, and say nothing about rent withholding. Local schemes, such as Manchester's licensing rules, may add further duties. Check with Manchester City Council.